Retina prosthesis

ABSTRACT

The invention provides a retinal prosthetic method and device that mimics the responses of the retina to a broad range of stimuli, including natural stimuli. Ganglion cell firing patterns are generated in response to a stimulus using a set of encoders, interfaces, and transducers, where each transducer targets a single cell or a small number of cells. The conversion occurs on the same time scale as that carried out by the normal retina. In addition, aspects of the invention may be used with robotic or other mechanical devices, where processing of visual information is required. The encoders may be adjusted over time with aging or the progression of a disease.

CROSS REFERENCE TO RELATED APPLICATION

This application is a continuation-in-part of International PatentApplication No. PCT/US2011/026526 (filed on Feb. 28, 2011) which in turnclaims the benefit under 35 U.S.C. §119(e) of U.S. ProvisionalApplication Nos. 61/308,681 (filed on Feb. 26, 2010), 61/359,188 (filedon Jun. 28, 2010), 61/378,793 (filed on Aug. 31, 2010), and 61/382,280(filed on Sep. 13, 2010).

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with U.S. Government support under GM0779awarded by the National Institute of Health (NIH), and under FEY019454Aawarded by the National Eye Institute. The U.S. Government has certainrights in the invention.

FIELD OF THE INVENTION

The present invention relates to methods and devices for restoring orimproving vision, and for treating blindness or visual impairment. Inparticular, the present invention relates to methods and devices forrestoring or improving vision using a set of encoders that producenormal or near-normal retinal output together with a high resolutiontransducer targeted to retinal cells.

BACKGROUND OF THE INVENTION

Retinal prosthetics are targeted for patients with retinal degenerativediseases, such as age-related macular degeneration (AMD), and retinitispigmentosa (RP), which together affect 2 million people in the US(Friedman et al., 2004; Chader et al., 2009) and 25 million worldwide(Chopdar et al., 2003). In both diseases, it is the input side of theretina that degenerates: cones degenerate in AMD and rods in RP.

What the prosthetics aim to do is bypass the degenerated tissue andstimulate the surviving cells, so that visual information can once againreach the brain. The main targets of the prosthetics are the retinalganglion cells and the retinal bipolar cells (Loewenstein et al., 2004;Gerding et al., 2007; Winter et al., 2007; Lagali et al., 2008; Chaderet al., 2009; Zrenner et al., 2009; Thyagarajan et al., 2010).

Currently, the main strategy for retinal prostheses involves theimplantation of electrode arrays into the patient's retina in closeproximity to either the bipolar cells or ganglion cells (Gerding et al.,2007; Winter et al., 2007; Chader et al., 2009; Zrenner et al., 2009).The patient is then outfitted with a camera/signal-processing devicethat takes images and converts them into electronic signals; the signalsare then passed to the electrodes, which stimulate the cells (reviewedin (Chader et al., 2009)). While the patients can see some light, theperformance of the devices is still quite limited: patients are, forexample, able to see spots and edges (Nanduri et al., 2008; Chader etal., 2009), which provide some ability for navigation and gross featuredetection, but nothing close to normal vision has been possible. (Withrespect to navigation, patients can detect light sources, such asdoorways, windows and lamps. With respect to detecting shapes, patientscan discriminate objects or letters if they span ˜7 degrees of visualangle (Zrenner et al., 2009); this corresponds to about 20/1400 vision(20/200 is the acuity-definition of legal blindness in most places).

Efforts to improve the electrode-based retinal prosthetics have beendirected primarily toward increasing their resolution; the focus hasbeen on decreasing the size of the electrodes and increasing theirdensity in the arrays (Chader et al., 2009), as currently, theelectrodes range from 50 and 450 microns in diameter (Kelly et al.,2009; Zrenner et al., 2009; Ahuja et al., 2010), which is 10 to 100times the size of a retinal cell. While there have been some increasesin resolution, the current technology does not achieve the resolution ofthe normal retina, as it is not yet practical to stimulate individualcells with electrodes, and the technical challenge is severe: finerelectrodes require more current, which leads to tissue burning (see, forexample, the title and agenda for a recent conference on retinalprosthetics: “The Eye and The Chip 2010: 2010 Special Emphasis onRetinal Stimulation Safety for Neuro-Prosthetic Devices”).

As an alternative to stimulating cells with electrodes, optogenetics hasbeen used. The optogenetics approach involves expression of proteinssuch as channelrhodopsin-2 (ChR2) or one of its derivatives in theganglion cells or bipolar cells. ChR2 is light sensitive; cellsexpressing it undergo voltage changes upon light activation, whichallows the cells to send electrical signals. (Bi et al., 2006; Lagali etal., 2008; Zhang et al., 2009; Tomita et al., 2010) This approach offersthe potential for much higher resolution—cells can, in principle, bestimulated individually. While experiments in animals have demonstratedthat the potential for high resolution is real, the achievement of nearnormal or even partially normal vision does not occur as indicated inseveral recent papers in the field (Bi et al., 2006; Lagali et al.,2008; Zhang et al., 2009; Thyagarajan et al., 2010; Tomita et al.,2010).

Little attention has been paid by either leading approach to driving thestimulators (either the electrodes or a channelrhodopsin) in a way thatclosely resembles endogenous signaling from retina to brain. Endogenousretinal signaling is complex. When the normal retina receives an image,it carries out a series of operations on it—that is, it extractsinformation from it and converts the information into a code the braincan read.

Current electrode-based devices have used much simpler signal processingthan the retina, e.g., they just convert light intensity at each pointin the image into pulse rate with linear scaling (Loewenstein et al.,2004; Fried et al., 2006; Kibbel et al., 2009; Ahuja et al., 2010).Because of this, the retinal output generated by these devices is verydifferent from normal retinal output; the brain is expecting signals inone code and is getting them in another.

Current optogenetic approaches are similarly limited. Efforts to improvethem have focused largely on developing the properties ofchannelrhodopsin (e.g., increasing its sensitivity to light and alteringits kinetics) and have not devoted significant effort to mimickingendogenous retinal signal processing (Bi et al., 2006; Lagali et al.,2008; Zhang et al., 2009; Thyagarajan et al., 2010; Tomita et al.,2010).

Thus, there exists a need to develop a retinal prosthesis that convertsvisual input into normal retinal output that the brain can readilyinterpret. The retinal prosthesis also needs to provide high resolutionsignaling, ideally targeting individual retinal cells such as retinalganglion cells. The present invention sets forth such a prosthesis; itcombines an encoding step that produces normal or near-normal retinaloutput together with high resolution transducer to provide normal ornear normal vision to the blind.

SUMMARY OF THE INVENTION

In one aspect, a method is disclosed comprising: receiving raw imagedata corresponding to a series of raw images; and processing the rawimage data with an encoder to generate encoded data, wherein the encoderis characterized by an input/output transformation that substantiallymimics the input/output transformation of one or more retinal cells of avertebrate retina.

In some embodiments, the encoder is characterized by an input/outputtransformation that substantially mimics the input/output transformationof one or more retinal cells of a vertebrate retina over a range ofinput that includes natural scene images, including spatio-temporallyvarying images.

In some embodiments, processing the raw image data with an encoder togenerate encoded data includes: processing the raw image data togenerate a plurality of values, X, transforming the plurality of Xvalues into a plurality of response values, lm, indicative of acorresponding response of a retinal cell in the retina, m, andgenerating the encoded data based on the response values. In someembodiments, the response values correspond to retinal cell firingrates. In some embodiments, the response values correspond to a functionof the retinal cell firing rates. In some embodiments, the responsevalues correspond to retinal cell output pulses. In some embodiments,the response values correspond to retinal cell generator potential,i.e., the output of the convolution of the image with the spatiotemporalfilter(s).

In some embodiments, processing the raw image data with an encoder togenerate encoded data includes: receiving images from the raw image dataand, for each image, rescaling the luminance or contrast to generate arescaled image stream; receiving a set of N rescaled images from therescaled image stream and applying a spatiotemporal transformation tothe set of N images to generate a set of retinal response values, eachvalue in the set corresponding to a respective one of the retinal cells;generating the encoded data based on the retinal response values.

In some embodiments, the response values include retina cell firingrates. In some embodiments N is at least 5, at least about 20, at leastabout 100 or more, e.g., in the range of 1-1,000 or any subrangethereof.

In some embodiments, applying a spatiotemporal transformation includes:convolving of the N rescaled images with a spatiotemporal kernel togenerate one or more spatially-temporally transformed images; andapplying a nonlinear function to the spatially-temporally transformedimages to generate the set of response values.

In some embodiments, applying a spatiotemporal transformation includes:convolving the N rescaled images with a spatial kernel to generate Nspatially transformed images; convolving the N spatially transformedimages with a temporal kernel to generate a temporal transformationoutput; and applying a nonlinear function to the temporal transformationoutput to generate the set of response values.

In some embodiments, the encoder is characterized by a set ofparameters, and where the values of the parameters are determined usingresponse data obtained experimentally from a vertebrate retina whilesaid retina is exposed to white noise and natural scene stimuli.

In some embodiments, the encoder is configured such that the Pearson'scorrelation coefficient between a test input stimulus and acorresponding stimulus reconstructed from the encoded data that would begenerated by the encoder in response to the test input stimulus is atleast about 0.35, 0.65, at least about 0.95, or more, e.g., in the rangeof 0.35-1.0 or any subrange thereof. In some embodiments, the test inputstimulus includes a series of natural scenes.

In another aspect, an apparatus is disclosed including: at least onememory storage device configured to store raw image data; at least oneprocessor operably coupled with the memory and programmed to execute oneor more of the methods described herein.

In some embodiments, a non-transitory computer-readable medium havingcomputer-executable instructions for implementing the steps of one ormore of the methods described herein.

The methods and systems of the present invention provide for restoringor improving vision. Vision is restored or improved using a method thatreceives a stimulus, transforms the stimulus into a set of codes with aset of encoders, transforms the codes into signals with an interface,which then activate a plurality of retinal cells with a high resolutiontransducer driven by the signals from the interface. Activation of theplurality of retinal cells results in retinal ganglion cell responses,to a broad range of stimuli, that are substantially similar to theresponses of retinal ganglion cells from a normal retina to the samestimuli.

The performance of the methods to restore or improve vision may have thefollowing characteristics: (i) the fraction correct on a forced choicevisual discrimination task performed using the codes is at least about95 percent, 65 percent or 35 percent of the fraction correct on theforced choice visual discrimination task performed using retinalganglion cell responses from a normal retina; or, (ii) the Pearson'scorrelation coefficient between a test stimulus and the stimulusreconstructed from the codes when the test stimulus was presented is atleast about 0.95, 0.65 or 0.35.

Alternatively, the performance of the methods to restore or improvevision may have the following characteristics: (i) the fraction correcton a forced choice visual discrimination task performed using retinalganglion cell responses from the activated retina is at least about 95percent, 65 percent, or 35 percent of the fraction correct on a forcedchoice visual discrimination task performed using retinal ganglion cellresponses from a normal retina; or (ii) the Pearson's correlationcoefficient between a test stimulus and the stimulus reconstructed fromretinal ganglion cell responses from the activated retina when the teststimulus is presented is at least about 0.95, 0.65 or 0.35.

The encoding step can include the following steps: (i) preprocessing thestimulus into a plurality of values, X; (ii) transforming the pluralityof X values into a plurality of firing rates, λ_(m), for a retinalganglion cell in the retina, m; and, (iii) generating a coderepresenting spikes from said firing rates. The encoding step caninclude a step for modifying the code with a burst elimination step. Thecode may be non-transiently stored during the burst elimination step.The burst elimination step can include the steps of: (i) defining theduration of a segment to be examined and a criterion number of pulsesfor a segment of said duration; (ii) counting pulses in the segment;and, (iii) if the number of pulses exceeds the criterion number,replacing the segment by an alternative in which the time between pulsesis approximately maximal.

The encoder can have parameters. The values of these parameters aredetermined using response data obtained from a retina while said retinais exposed to white noise and natural scene stimuli.

The code can be transformed into output using an interface where theoutput is a plurality of visible light pulses. The transducer can be avisible light responsive element, such as, for example, a protein. Theprotein can be Channelrhodopsin-1, Channelrhodopsin-2, LiGluR, ChETA,SFO (step function opsins), OptoXR (light-sensitive GPCR), VolvoxChannelrhodopsin-1, Volvox Channelrhodopsin-2, ChIEF, NpHr, eNpHR, orcombinations of any of them.

The gene encoding the protein can be introduced into the cell using aviral vector. The viral vector can be recombinant adeno-associatedvirus. The gene can be expressed selectively in at least one retinalganglion cell type. In one embodiment, the gene can be selectivelyexpressed using a two vector cre-lox system, where the expressionpatterns of the two vectors overlap only within the selected cell type.In this embodiment, the two vectors are: (a) a first vector having aninverted gene expressing a light-sensitive protein that is flanked byloxP sites oriented in opposite directions and that is under theregulation of a promoter for a second gene that is expressed at least inthe selected cell type; and (b) a second vector comprising a Crerecombinase that is under the regulation of a promoter for a third genethat is expressed at least in the selected cell type and anonoverlapping set of other cell classes.

The device implementing the method to restore or improve vision can beused to treat a subject with a retinal degenerative disease, such asmacular degeneration or retinitis pigmentosa. When treated, the subjectis able to achieve at least about 95%, 65% or 35% normal visual acuityas measured with EVA or the ETDRS protocols. Alternatively, whentreated, the subject experiences a change of a factor of two or moreusing the pattern VEP test or Sweep VEP test.

The methods of the invention also provide for a method for activating aplurality of retinal cells involving, receiving a stimulus, transformingthe stimulus into a set of codes with a set of encoders, transformingthe codes into signals with an interface and activating a plurality ofretinal cells with a high resolution transducer driven by the signalsfrom the interface. Activation of the plurality of retinal cells resultsin responses to a broad range of stimuli, where the stimuli compriseartificial and natural stimuli, and said responses are substantiallysimilar to the responses of normal retinal cells to the same stimuli.

Alternatively, the performance of the method to activate a plurality ofretinal cells may exhibit the following characteristics: (i) thefraction correct on a forced choice visual discrimination task performedusing the codes is at least about 95 percent, 65 percent, or 35 percentof the fraction correct on a forced choice visual discrimination taskperformed using retinal ganglion cell responses from a normal retina, orwhere the Pearson's correlation coefficient between a test stimulus andthe stimulus reconstructed from the codes when the test stimulus waspresented is at least about 0.95, 0.65 or 0.35.

The methods and systems of the invention also provide for an apparatusfor restoring or improving vision in a subject in need thereof, wherethe apparatus has: (i) a device for receiving a stimulus; (ii) aprocessing device comprising: (a) non-transient computer readable mediastoring a set of encoders to generate a set of codes from the stimulus,(b) at least one processor, and (c) non-transient computer readablemedia storing the codes; (iii) an interface for converting the codesinto an output; and, (iv) a high resolution transducer for activating aplurality of retinal cells. The performance of the apparatus forrestoring or improving vision is such that activation of the pluralityof retinal cells results in retinal ganglion cell responses, to a broadrange of stimuli, that are substantially similar to the responses ofretinal ganglion cells from a normal retina to the same stimuli.Alternatively, the performance of the apparatus exhibits the followingcharacteristics: (i) the fraction correct on a forced choice visualdiscrimination task performed using the codes is at least about 95percent, 65 percent or 35 percent of the fraction correct on a forcedchoice visual discrimination task performed using retinal ganglion cellresponses from a normal retina; or (ii) the Pearson's correlationcoefficient between a test stimulus and the stimulus reconstructed fromthe codes when the test stimulus was presented is at least about 0.95,0.65 or 0.35. When treated with the apparatus for restoring or improvingvision, the subject can achieve at least about 35% normal visual acuityas measured with EVS or the ETDRS protocols. Alternatively, the treatedsubject experiences a change of a factor of two or more using thepattern VEP test or Sweep VEP test. The apparatus for restoring orimproving vision can be used to treat a subject who has a retinaldegenerative disease, such as macular degeneration or retinitispigmentosa.

The methods and systems of the present invention also provide for anon-transitory computer readable medium having computer-executableinstructions. The computer-excutable instructions are a set ofinstructions for converting at least one stimulus into non-transitorycodes, where the code is capable of activating a plurality of retinalcells with a high resolution transducer. The performance of the systemis such that when measured, the fraction correct on a forced choicevisual discrimination task performed using the codes is at least about35 percent of the fraction correct on a forced choice visualdiscrimination task performed using retinal ganglion cell responses froma normal retina, or the Pearson's correlation coefficient between a teststimulus and the stimulus reconstructed from the codes when the teststimulus was presented is at least about 0.35. The set of instructionshas parameters and the values of these parameters may be determinedusing response data obtained from a retina while said retina is exposedto white noise and natural scene stimuli.

The methods and systems of the present invention also provide fornon-transitory computer-readable medium having computer-executableinstruction which has a signal, corresponding to a stimulus, forcontrolling at least one transducer capable of activating at least onecell in an impaired retina to produce a response which is substantiallysimilar to a response to the stimulus of a corresponding ganglion cellin a normal retina. The signal can be a set of codes, where whenmeasured for performance, the fraction correct on a forced choice visualdiscrimination task performed using the codes is at least about 35percent of the fraction correct on a forced choice visual discriminationtask performed using retinal ganglion cell responses from a normalretina, or the Pearson's correlation coefficient between a test stimulusand the stimulus reconstructed from the codes when the test stimulus waspresented is at least about 0.35.

The methods and systems of the present invention also provide for amethod for generating a representation of a stimulus using an encoderfor a retina. The methods comprises the following steps: (i)preprocessing the stimulus into a plurality of values, X; (ii)transforming the plurality of X values into a plurality of firing rates,λ_(m); and, (iii) converting the firing rate, λ_(m), to a code. In thiscase, the performance of the method may be measured as follows: (i) thefraction correct performance on a discrimination task by the output ofthe encoder is within 35 percent of the fraction correct performance ona discrimination task by a normal retina; (ii) the Pearson's correlationcoefficient between the stimulus reconstructed from the output of theencoder and the original stimulus will be at least about 0.35, or whereperformance of the output of the encoder on an error pattern test is atmost about 0.04. The transformation step may involve spatiotemporallytransforming the plurality of X values into a plurality of firing rates,λ_(m), where, λ_(m), for each retinal ganglion cell in the retina, m, isa function of L_(m) which is a linear filter corresponding to thespatiotemporal kernel from a mth retinal ganglion cell, and N_(m) is afunction that describes the mth retinal ganglion cell's nonlinearity.There may be a plurality of encoders e_(m), where e_(m) is the encoderfor the mth ganglion cell. The code may have a discrete plurality ofbits forming a bit stream. Alternatively, the code is a continuous wave.

The stimulus can be electromagnetic radiation. For example, theelectromagnetic radiation can be visible light. The code can betransformed using an interface into output which may be a plurality ofvisible light pulses. Activation of a plurality of cells in a retinawith the plurality of visible light pulses can generate at least onefirst set of spike trains, where at least a fraction of the cells in theretina have at least one transducer which is a visible light responsiveelement.

The method for generating a representation of a stimulus using anencoder for a retina can further involve driving activation of aplurality of cells in a retina with the plurality of visible lightpulses to generate at least one first set of spike trains, where atleast a fraction of the cells in the retina have at least one transducercomprising at least one visible light responsive element. The cells canbe retinal ganglion cells. The visible light responsive element can besynthetic photoisomerizable azobenzene regulated K+ (SPARK),deoplarizing SPARK (D-SPARK) or combinations of any of the foregoing.The visible light responsive element may be a protein such as,Channelrhodopsin-1, Channelrhodopsin-2, LiGluR, ChETA, SFO (stepfunction opsins), OptoXR (light-sensitive GPCR), VolvoxChannelrhodopsin-1, Volvox Channelrhodopsin-2, ChIEF, NpHr, eNpHR orcombinations of any of the foregoing. The proteins, genes encoding forthem and the viral vectors are all as mentioned previously. The stimuluscan vary in a spatio-temporal fashion or may be static. The presentinvention also provides for a method for determining a set of parametersfor an encoder which has the steps of: (a) recording electrical signaldata comprising action potential times from retinal ganglion cells of aretina while the retina is exposed to white noise and natural scenestimuli and storing the data; (b) calculating the reverse correlationbetween the ganglion cell action potential times and the stimulusintensity is calculated, to determine a starting set of values for thelinear filter L_(m); (c) treating L_(m) as a product of a spatialfunction and a temporal function wherein the spatial function isparameterized as a grid of weights, and the temporal function isparameterized as the sum of weighted temporal basis functions and N_(m)is assumed to be an exponential function to ensure there are no localmaxima; (d) calculating the likelihood for this set of parameters forthe given stimulus and recorded ganglion cell's responses; (e)identifying the initial optimal parameters for the spatial function,temporal function, and exponential nonlinearity by maximizing thelikelihood of these parameters; (f) replacing the exponentialnonlinearity by a cubic spline; (g) optimizing the parameters of thespline to maximize the likelihood; (h) optimizing the parameters of thespatial and temporal functions to maximize the likelihood while holdingthe results of step (g) constant; (i) step (g) is repeated while holdingresults of step (h) constant, and step (h) is repeated; and, (j) step(i) is repeated until the change in likelihood from the two steps isless than an arbitrarily chosen small number. The foregoing method maybe embodied in a nontransitory computer-readable medium havingcomputer-executable instructions for determining values for a pluralityof parameters which are used for converting at least one first stimulusinto a non-transitory code, the parameters for a linear filter, L_(m), aspatial function and a temporal function, where the parameters aredetermined by the steps comprising: (a) recording electrical signal datacomprising action potential times from retinal ganglion cells of aretina while said retina is exposed to white noise and natural scenestimuli and storing said data; (b) calculating a reverse correlationbetween retinal ganglion cell action potential times and intensity ofeach stimulus, to determine a starting set of values for the linearfilter L_(m); (c) establishing a set of parameters for a spatialfunction; (d) establishing a set of parameters for a temporal function;(e) calculating the likelihood for the set of parameters for the spatialfunction and the temporal function for a given stimulus and recordingresponses from the retinal ganglion cell; and, (f) finding optimal setsof parameters for the spatial function, temporal function, andnonlinearity by maximizing the likelihood of the parameters.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic of one embodiment of the prosthetic method. Thestimulus is shown on the left, followed by an image—the capturedstimulus. The captured stimulus is then processed through a set ofencoders, which in turn drive an interface device. The interface devicethen fires light pulses at retinal ganglion cells that have beentransfected with a light-sensitive element, channelrhodopsin-2 (ChR2).The retina produces spike patterns similar to those produced by ahealthy retina.

FIG. 2 is a schematic of an embodiment of the device. On the outwardface of each lens region in the pair of eyeglasses is a camera; signalsfrom the cameras are directed to the processing device, which, in thisembodiment, is located on the arm of the glasses. The processing devicecontrols the light array, which is on the inner face of each lensregion.

FIG. 3 shows that the amount of information carried by the encoders (themodel cells) closely matches that carried by their real cellcounterparts. For this analysis, we used three stimulus sets—driftinggratings that varied in temporal frequency, drifting gratings thatvaried in spatial frequency, and natural scenes. For each cell, wecalculated the mutual information between its model cell's responses andthe stimuli and plotted it against the mutual information between thereal cell's responses and the stimuli (n=106, 118, and 103, for thethree sets of stimuli respectively; stimulus entropy for each was 5bits; bin sizes ranged from 250 to 31 ms).

FIG. 4 (FIGS. 4-1, 4-2, and 4-3) shows that the posterior stimulusdistributions of the encoders (the model cells) closely match those oftheir real cell counterparts. A. For each cell, we plotted a pair ofmatrices. The matrix on the left gives the posterior for the modelcell's responses (averaged over all responses); the matrix on the rightgives the same for the real cell's responses. The histogram next to thepair gives a measure of the distance between them. Briefly, for eachrow, we computed the mean squared error (MSE) between the model'sposterior and the real cell's posterior and then normalized it bydividing it by the MSE between the real cell's posterior and a randomlyshuffled posterior. A value of 0 indicates that the two rows areidentical. A value of 1 indicates that they are as different as tworandomly shuffled rows. (Because of data limitation, occasional cellsshowed values higher than 1.) The vertical light grey line indicates themedian value of the histogram. B. Histogram of the median values for allcells in the data set, and histogram of K-L divergences for all cells inthe data set (n=106, 118 and 103 cells for the stimuli, respectively).

FIG. 5 shows that the encoders (the model cells) make the samepredictions as the real cells. Top left, the model indicates that ONcells are better able to distinguish among low temporal frequencies thanOFF cells under scotopic conditions, whereas OFF cells are better ableto distinguish among high temporal frequencies than ON cells. Bottomleft, the real cells indicate the same. Top, looking across scotopic andphotopic conditions, the model indicates that these differences in thebehavior only occur under scotopic conditions: the two cell classesperform approximately equally well under photopic conditions. Bottom,looking across scotopic and photopic conditions, the real cells indicatethe same. Top, looking across the two conditions again, the model showsthat ON and OFF cells perform well only for a narrow range offrequencies under scotopic conditions, but over a wide range underphotopic conditions. Bottom, looking across the two conditions, again,this prediction held for the real cells as well. Predictions were madewith increasing numbers of cells until there was indication ofperformance saturation. Error bars are SEM.

FIG. 6 shows that the encoders (the model cells) predict the shift inoptomotor performance. Left, the model predicts a shift toward highertemporal frequencies as the animal moves from scotopic to photopicconditions. Right, the animals' behavioral performance shifted to highertemporal frequencies, as predicted (n=5 animals). The prediction wasrobust from 1 cell to saturation (20 cells).

FIG. 7 shows that ganglion cell responses produced by the retinaprosthesis closely match those produced by normal retina, whereasganglion cell responses produced by the standard optogenetic approach(i.e., using ChR2 as the transducer) do not match those produced bynormal retina. Movies of natural scenes were presented to three groupsof mouse retinas: retinas from normal mice, retinas from blind mice thatwere treated with the retina prosthesis (i.e. the blind retinas wereexpressing ChR2 in the ganglion cells and were stimulated with moviesthat had been processed by the encoders), and retinas from blind micetreated with the standard optogenetic approach (i.e. the blind retinaswere expressing ChR2 in the ganglion cells but were stimulated withmovies that had not been processed by the encoders). Then spike trainswere recorded from the ganglion cells of each group.

FIG. 8 shows that the performance of the retina prosthesis on a visualdiscrimination task closely matches the performance of the normalretina, whereas the performance of the standard optogenetic method doesnot. A. Confusion matrices generated when the testing set was obtainedfrom the normal WT retina. On the left are the matrices for individualganglion cells, on the right, for a population of cells (20 cells).Fraction correct for the population was 80%. B. Confusion matricesgenerated when the testing set was obtained from the encoders (note thatthese encoders were built from the input/output relations of the WTretina used in panel A). Fraction correct was 79%. C. Confusion matricesgenerated when the testing set was generated from a blind retina, wherethe ganglion cells were driven with the encoder+transducer. (ChR2).Fraction correct was 64%. D. Confusion matrices generated when thetesting set was generated from a blind retina, where the ganglion cellswere driven with the standard optogenetic method (i.e., ChR2 alone withno encoders). Fraction correct was 7%.

FIG. 9 shows that an image reconstructed from the responses of theretinal prosthesis closely matches the original image while an imagereconstructed from the responses of the standard optogenetic method doesnot. While the brain does not necessarily reconstruct images,reconstructions serve as a convenient way to compare methods and give anapproximation of the level of visual restoration possible with eachapproach. A. Original image. B. Image reconstructed from the responsesof the encoders. C. Image reconstructed from the responses of theencoders+transducers (ChR2). D. Image reconstructed from the responsesof the standard optogenetic approach (just ChR2, as in above figures).Note that panel B is the critical panel, as it shows the output of theencoders, which could be teamed up with different kinds of transducers.The reconstructions were carried out on our processing cluster in blocksof 10×10 or 7×7 checks. As mentioned in the text, we used maximumlikelihood, that is, for each block, we found the array of gray valuesthat maximized the probability of the observed responses (for highdimensional searches, following Paninski et al. 2007).

FIG. 10 shows that tracking occurs with the retina prosthesis. A.Baseline drift (no stimulus present). As mentioned in the text, blindanimals show a drift in eye position, similar to the drift observed withblind humans. B Response to drifting grating presented using thestandard optogenetic method (i.e., presented on the screen as it is). C.Response to drifting grating presented using the retina prosthesis(i.e., presented on the screen in its encoded form). When the image hasbeen converted into the code used by the ganglion cells, the animal cantrack it. Top row, raw eye position trace, a representative example.Middle row, smooth component (saccades and movement artifacts removed,see raw trace above). Bottom row, average trajectory across all trials(n=15, 14, and 15 trials, respectively).

FIG. 11 shows a schematic of the device. A camera (top) captures stimulifrom the visual field. The signals from the camera are fed to aprocessing device that executes the encoders. Execution of the encodersproceeds in a series of steps, indicated in the figure as modules:preprocessing, spatiotemporal transformation, and spike generation. Theoutput of the spike generation step is nontransiently stored inpreparation for conversion to a format suitable for the transducers,which includes a burst elimination step. The output is then converted tothe format suitable for the transducers in the interface, and theinterface then sends its converted signals to the transducers. Arrowsshow the flow of signals from specific regions of the visual fieldthrough the modules of the encoders, through the interface device, tothe transducers, which are in the retinal cells. The overlapping circlesindicate that the encoders carry information from overlapping regions ofthe visual field, representing images in a way that is analogous to thatof the normal retina.

FIG. 12 illustrates the conversion from image to light pulses for anexample encoder. A shows an example movie. B shows the pre-processedmovie and indicates the position of the example encoder that producesthe output in C-E. C shows the output of the spatiotemporaltransformation step. D shows the output of the spike generation step. Eshows the light pulses that correspond to the output produced by thespike generation step.

FIG. 13 shows that the responses produced by encoders generated frommonkey retina to natural movies closely match those produced by normalmonkey retina. Movies of natural scenes were presented to the normalmonkey retina and the virtual retina. The top row shows spike trainsfrom normal monkey ganglion cells; the bottom from their correspondingmodel cells (i.e., their encoders).

FIG. 14 shows that the performance of the monkey encoders on a visualdiscrimination task (same task as in FIG. 8) closely matches theperformance of normal monkey ganglion cells. A. Confusion matricesgenerated when the testing set was obtained from the normal monkeyretina. On the left are the matrices for individual ganglion cells, onthe right, for a population of cells (10 cells). Fraction correct forthe population was 83%. B. Confusion matrices generated when the testingset was obtained from the encoders that were generated from monkeyganglion cells. Fraction correct was 77%. All analysis was performed asExample 8, FIG. 8. Fraction correct using encoder responses was thus92.8% of fraction correct using normal monkey ganglion cell responses.

FIG. 15 shows that ganglion cell responses produced by theencoders+transducers follow the encoded output with high fidelity. Theencoder's output was converted into a stream of light pulses, which werepresented to a retina extracted from a doubly transgenic mouse that isblind and that expresses ChR2 in the ganglion cells. A. Light pulses andthe corresponding ganglion cell output. For each pair of rows, the toprow shows the times of the light pulses, while the bottom row shows thetimes of the action potentials produced by the ChR2-expressing ganglioncell. Each dot represents the occurrence of a light pulse or ganglioncell action potential. B. Expansion of the circled regions from (A),showing one-to-one correspondence between light pulses and actionpotentials. The action potentials followed the light pulses, andtherefore, the encoder, with high fidelity.

FIGS. 16A-16F illustrate the performance of a retinal encoder modelswhen tested with movies of natural scenes, including landscapes, peoplewalking, etc. In each figure, the performance of a conventionallinear-nonlinear (LN) model is shown on the left, and the performance ofthe linear-nonlinear (LN) model of the type described in thisapplication is shown on the right. Performance is shown via raster plotsand peri-stimulus time histograms (PSTHs).

DETAILED DESCRIPTION OF THE INVENTION

The present invention provides for a method and device for restoring orimproving vision, increasing visual acuity, or treating blindness orvisual impairment, or activating retinal cells. The method comprisescapturing a stimulus, encoding the stimulus, transforming the code intotransducer instructions at an interface, and transducing theinstructions to retinal cells. The device comprises a way to capture astimulus, a processing device executing a set of encoders, an interface,and a set of transducers, where each transducer targets a single cell ora small number of cells; the set of transducers is referred to as a highresolution transducer. In one embodiment, each encoder executes apreprocessing step, a spatiotemporal transforming step as well as anoutput-generating step. The present method can be used for a retinalprosthesis to generate representations for a broad range of stimuli,including artifical and natural stimuli.

The present methods and devices may process any type of stimulus. Forexample, the stimulus may include visible light, but may also includeother types of electromagnetic radiation such as infrared, ultravioletor other wavelengths across the electromagnetic spectrum. The stimulusmay be a single image or a plurality of images; additionally, the imagesmay be static or may vary in a spatiotemporal fashion. Simple shapessuch as diagrams or comparatively complex stimuli such as natural scenesmay be used. Additionally, the images may be grayscale or in color orcombinations of grey and color. In one embodiment, the stimuli maycomprise white noise (“WN”) and/or natural stimuli (“NS”) such as amovie of natural scenes or combinations of both.

The stimulus is converted or transformed into a proxy of normal retinaloutput, that is, a form of output the brain can readily interpret andmake use of as a representation of an image. The conversion occurs onabout the same time scale as that carried out by the normal ornear-normal retina, i.e., the initial retinal ganglion cell response toa stimulus occurs in a time interval ranging from about 5-300 ms. Themethods and devices of the present invention can help restorenear-normal to normal vision, or can improve vision, including bothgrayscale vision and color vision, in a patient or affected mammal withany type of retinal degenerative disease where retinal ganglion cells(which may also be referred to herein as “ganglion cells”) remainintact. Nonlimiting examples of retinal degenerative diseases includeretinitis pigmentosa, age-related macular degeneration, Usher syndrome,Stargardt macular dystrophy, Leber congenital amaurosis and Bardet-Biedlsyndrome, retinal detachment, and retinal vessel occlusion.

Diseases in which retinal degeneration occurs as a complication include:Snowflake vitreoretinal degeneration; Choroidal neovasculatizationcaused by adult-onset foveomacular dystrophy; Bietti crystallinecorneoretinal dystrophy; and diabetic retinopathy. A partial list ofdiseases in which retinal degeneration occurs as a symptom include:Aceruloplasminemia; Adrenoleukodystrophy; Alstrom disease; AlströmSyndrome; Asphyxiating Thoracic Dystrophy; Bonneman-Meinecke-Reichsyndrome; Bonnemann-Meinecke-Reich syndrome; CDG syndrome type 1A;Chorioretinopathy dominant form—microcephaly;Choroideremia—hypopituitarism; Congenital disorder of glycosylation type1A; Congenital Disorders of Glycosylation Type Ia; Cystinosis;Hypotrichosis, syndactyly and retinal degeneration; Jeune syndrome;Mucolipidosis IV; Mucolipidosis type 4; Mucopolysaccharidoses;Muscle-eye-brain syndrome; Neonatal ALD; Olivopontocerebellar atrophytype 3; Osteopetrosis, autosomal recessive 4; Pigmentary retinopathy;Pseudoadrenoleukodystrophy; Retinoschisis, X-linked; Retinoschisis1,X-linked, Juvenile; Santavuori Disease; Spastic paraplegia 15, autosomalrecessive; and Werner syndrome

The present methods and devices can be used to treat any mammaliansubject who has a fraction of retinal ganglion cells, part of the opticnerve originating therefrom as well as some portion of other functionalcentral visual system processing functions remaining intact. Conversely,the range of loss of retinal ganglion cells that is treatable with themethods and devices of the present invention can include only a portionof the total number of retinal ganglion cells or may encompass the totalnumber of retinal ganglion cells present in the retina.

The retina prosthesis, like the normal retina, is an image processor—itextracts essential information from the stimuli it receives, andreformats the information into patterns of action potentials the braincan understand. The patterns of action potentials produced by the normalretinal are in what is referred to as the retina's code or the ganglioncell's code. The retina prosthesis converts visual stimuli into thissame code, or a close proxy of it, so that the damaged or degeneratedretina can produce normal or near-normal output. Because the retinaprosthesis uses the same code as the normal retina or a close proxy ofit, the firing patterns of the ganglion cells in the damaged ordegenerated retina, that is, their patterns of action potentials are thesame, or substantially similar, to those produced by normal ganglioncells. A subject treated with the present devices will have visualrecognition ability closely matching the ability of a normal ornear-normal subject.

As measured by a variety of different criteria described below, themethods and devices of the present invention reproduce normal or nearnormal ganglion cell output for a broad range of stimuli, includingartifical and natural stimuli. In the retinal prosthetic method, themethods of the invention use an encoding step, an interfacing step, anda transducing step. The methods and devices of the present invention candrive the activation of different retinal cell classes, including, butnot limited to, retinal ganglion cells and retinal bipolar cells.

In one embodiment, the prosthesis targets retinal ganglion cells. Inthis embodiment, the encoding step converts visual stimuli into thecode, or a close proxy of the code, used by the ganglion cells, and thetransducer, via an interface, drives the ganglion cells to fire as thecode specifies. The result is that the damaged or degenerated retinaproduces normal or near normal output, that is, normal or near normalfiring patterns. In another embodiment, the prosthesis targets theretinal bipolar cells (i.e., the transducer is targeted to the retinalbipolar cells, which may also be referred to herein as “bipolar cells”).In this case, the encoding step occurs one stage earlier, that is, theencoding step converts visual stimuli into a code that will drive thebipolar cells to drive the ganglion cells to produce normal output. Theuse of other codes is also possible. In both cases, the prosthesiscomprises a set of encoders and a set of transducers that interact: theencoders drive the transducers. As described below, the encoders drivethe transducers via an interface. The result is a method that causes theretinal output cells to produce normal or near normal firing patterns,and deliver normal or near normal visual signals to the brain.

Different encoders may be used, since there are different types ofretinal cells. Differences may correspond to a particular cell type orto the cell position on the retina. When a retina prosthesis has morethan one encoder, the encoders may operate in parallel, eitherindependently or through at least one or more coupling mechanisms.

As mentioned above, in one embodiment, the retinal prosthesis targetsthe retinal ganglion cells. In this embodiment, the retinal ganglioncells of a subject (e.g., a blind patient) are first engineered via genetherapy to express a transducer, e.g., light-sensitive protein (forexample, ChR2). The subject then wears glasses that carry a camera, aprocessing device executing a set of encoders (one or more), and aninterface for generating light pulses. The camera captures images(stimuli), and passes them through the set of encoders. The encodersperform a series of operations on the stimuli and convert them into acoded output, that is, patterns (also referred to as streams) ofelectrical pulses that correspond to the patterns (or streams) of actionpotentials the normal ganglion cells would produce to the same stimuli.The streams of electrical pulses are then converted into streams oflight pulses to drive the ChR2-expressing cells in the subject's retina.FIG. 1 shows schematically the steps of converting a stimulus (an image)into streams of electrical pulses, which are then converted into streamsof light pulses, which then drive the transducers in the retinal cells.FIG. 2 shows an embodiment of the device as it would be provided topatients (the external device that interacts with the transducersoperating in vivo.)

Alternatively, instead of the patient receiving gene therapy to providethe transducer, ChR2, electrodes are implanted in the patient's retinain close proximity to the ganglion cells or bipolar cells. In this case,the patient then wears glasses that carry a camera and a processingdevice executing a set of encoders, and the electrical pulses or bitstreams are stored in memory and converted to signals that direct theelectrodes to emit electrical pulses that ultimately drive the ganglioncells to fire.

The present methods and devices can be used in a mammal, such as ahuman. Mammals include, but are not limited to, a rodent (e.g., a guineapig, a hamster, a rat, a mouse), a primate, a marsupial (e.g., kangaroo,wombat), a monotreme (e.g., duckbilled platypus), murine (e.g., amouse), a lagomorph (e.g., a rabbit), canine (e.g., a dog), feline(e.g., a cat), equine (e.g., a horse), porcine (e.g., a pig), ovine(e.g., a sheep), bovine (e.g., a cow), simian (e.g., a monkey or ape), amonkey (e.g., marmoset, baboon), an ape (e.g., gorilla, chimpanzee,orangutang, gibbon).

The methods and devices of the present invention may also be usedtogether with robotic or other type of mechanical devices, whereprocessing of visual information or light patterns is required.

The algorithms and/or parameters of the encoders may vary from onepatient to another, and may be adjusted over time with aging or theprogression of the disease. In addition, a single patient may beequipped with multiple encoders in a single prosthesis where theencoders vary by the spatial position on the retina or other factors,such as cell type, as described herein. The present invention allowsability to conveniently and safely alter the algorithm from outside thebody of the patient. Adjustment of the algorithm may be done by one ofordinary skill in the art.

The encoder (or the encoding step) and the transducer (or thetransducing step) are described below.

Encoders

An encoder is an input/output model for a cell in the retina (e.g., aganglion cell or a bipolar cell). It provides the stimulus/responserelationship. The encoder operates as an algorithm; the algorithm may beexecuted by a processing device with dedicated circuitry and/or usingcomputer-readable media, as described herein.

In one embodiment, the encoders are input/output models for the ganglioncells. These encoders comprise an algorithm that converts stimuli intopatterns of electrical signals that are the same, or substantiallysimilar, to those produced by normal ganglion cells to the same stimuli.The retinal prosthetic can use multiple encoders which can be assembledin a parallel manner as shown, for example, in FIG. 11, where differentsegments of the stimulus (or put another way, different regions of thevisual field) are run through separate encoders, which, in turn, controldifferent, specified transducers. In this embodiment, each encoder mayhave parameters suited for its targeted transducers, which may, forexample, take into account the location and/or type of retinal cell orcells being emulated by the encoder or being driven by the encoder'soutput. The term “code” can refer to a pattern of electrical pulses thatcorresponds to a pattern of action potentials (also referred to as spiketrains) that the retina produces in response to a stimulus. The term“code” may refer to bit streams corresponding to a pattern of spiketrains. Each bit may correspond to the activity of one neuron (e.g., 1means the neuron fires; 0 means the neuron does not fire). The code mayalso be a continuous wave. Any type of waveform may be encompassed bythe present invention, including nonperiodic waveforms and periodicwaveforms, including but not limited to, sinusoidal waveforms, squarewaveforms, triangle waveforms, or sawtooth waveforms.

The general overview of operations performed by one embodiment of theencoder is shown in the flowchart below.

Preprocessing Step

This is a rescaling step, which may be performed in a preprocessormodule of the processing device, that maps the real world image, I, intoquantities, X, that are in the operating range of the spatiotemporaltransformation. Note that I and X are time-varying quantities, that is,I(j,t) represents the intensity of the real image at each location j andtime t, and X(j,t) represents the corresponding output of thepreprocessing step. The preprocessing step may map as follows: I(j,t) ismapped to X(j,t) by X(j,t)=a+bI(j,t), where a and b are constants chosento map the range of real world image intensities into the operatingrange of the spatiotemporal transformation.

The rescaling can also be done using a variable history to determine thequantities a and b, and a user-operated switch can be used to set thevalues of these quantities under different conditions (e.g., differentlighting or different contrast).

For grayscale images, both I(j,t) and X(j,t) have one value for eachlocation j and time t.

For color images, the same strategy is used, but it is appliedseparately to each color channel, red, green, and blue. In oneembodiment, the intensity I(j,t) has three values (I₁, I₂, I₃) for eachlocation j and time t, where the three values I₁, I₂, I₃ represent thered, green, and blue intensities, respectively. Each intensity value isthen rescaled into its corresponding X value (X₁, X₂, X₃) by the abovetransformation.

Spatiotemporal Transformation Step

In one embodiment, the transformation is carried out using alinear-nonlinear cascade (reviewed in Chichilnisky E J 2001; Simoncelliet al 2004), where the firing rate, λ_(m), for each ganglion cell, m, isgiven byλ_(m)(t;X)=N _(m)((X*L _(m))(j,t)  (1)where * denotes spatiotemporal convolution, L_(m) is a linear filtercorresponding to the mth cell's spatiotemporal kernel, and N_(m) is afunction that describes the mth cell's nonlinearity, and, as in theprevious section X is the output of the preprocessing step, j is thepixel location, and t is time. The firing rate, λ_(m), is converted intoa code that is used to drive the interface (discussed subsequently).This spatiotemporal transformation step may be performed by aspatiotemporal transforming module of the processing device.

L_(m) is parameterized as a product of a spatial function and a temporalfunction. For example, in one embodiment, the spatial function consistsof a weight at each pixel on a grid (e.g., the digitized image in acamera), but other alternatives, such as a sum of orthogonal basisfunctions on the grid, can be used. In this embodiment, the gridconsists of a 10 by 10 array of pixels, subserving a total of 26 by 26degrees of visual space (where each pixel is 2.6 by 2.6 degrees invisual space), but other alternatives can be used. For example, becausethe area of visual space that corresponds to a retinal ganglion cellvaries with spatial position on the retina and from species to species,the total array size can vary (e.g., from at or around from 0.1 by 0.1degree to 30 by 30 degrees, which corresponds to at or around 0.01 by0.01 degree to 3 by 3 degrees in visual space for each pixel in a 10 by10 array of pixels.) It is appreciated that the angle ranges and size ofthe pixel array are only provided for illustration of one particularembodiment and that other ranges of degrees or size of pixel arrays areencompassed by the present invention. For any chosen array size, thenumber of pixels in the array can also vary, depending on the shape ofthe area in visual space that the cell represents (e.g., an array of ator around from 1 by 1 to 25 by 25 pixels). Similarly, the temporalfunction consists of a sum of weights at several time bins and raisedcosine functions in logarithmic time at other time bins (Nirenberg etal. 2010; Pillow J W et al. 2008). Other alternatives, such as a sum oforthogonal basis functions, can also be used.

In this embodiment, the time samples span 18 time bins, 67 ms each, fora total duration of 1.2 sec, but other alternatives can be used. Forexample, because different ganglion cells have different temporalproperties, the duration spanned by the bins and the number of binsneeded to represent the cell's dynamics can vary (e.g., a duration at oraround from 0.5 to 2.0 sec and a number of bins at or around from 5 to20). Temporal properties can also vary across species, but thisvariation will be encompassed by the above range.

Eq. 1 can also be modified to include terms that modify the encoder'soutput depending on its past history (i.e., the spike train alreadyproduced by cell m), and on the past history of the output of otherganglion cells (Nirenberg et al. 2010; Pillow J W et al. 2008).

For both sets of parameters for L (spatial and temporal), the choice ofresolution (pixel size, bin size) and span (number of pixels, number oftime bins) is determined by two factors: the need to obtain a reasonablyclose proxy for the retina's code, and the need to keep the number ofparameters small enough so that they can be determined by a practicaloptimization procedure (see below). For example, if the number ofparameters is too small or the resolution is too low, then the proxywill not be sufficiently accurate. If the number of parameters is toolarge, then the optimization procedure will suffer from overfitting, andthe resulting transformation (Eq. 1) will not generalize. The use of asuitable set of basis functions is a strategy to reduce the number ofparameters and hence avoids overfitting, i.e., a “dimensionalityreduction” strategy. For example, the temporal function (that covers 18time bins, 67 ms each) may be parameterized by a sum of 10 weights andbasis functions; see section “Example 1, Method of building the encoder”and (Nirenberg et al., 2010; Pillow J W et al. 2008)

The nonlinearities N_(m) are parameterized as cubic splines, but otherparameterizations can be used, such as, piecewise linear functions,higher-order splines, Taylor series and quotients of Taylor series. Inone embodiment, the nonlinearities N_(m) are parameterized as cubicspline functions with 7 knots. The number of knots is chosen so that theshape of the nonlinearity is accurately captured, while overfitting isavoided (see above discussion of overfitting). At least two knots arerequired to control the endpoints, and thus the number of knots canrange from about 2 to at least about 12. Knots are spaced to cover therange of values given by the linear filter output of the models.

For the spatiotemporal transformation step, in addition to thelinear-nonlinear (LN) cascade described above, alternative mappings arealso within the scope of the present invention. Alternative mappingsinclude, but are not limited to, artificial neural networks and otherfilter combinations, such as linear-nonlinear-linear (LNL) cascades.Additionally, the spatiotemporal transformation can incorporate feedbackfrom the spike generator stage (see below) to provide history-dependenceand include correlations among the neurons as in (Pillow J W et al.2008; Nichols et al, 2010). For example, this can be implemented byconvolving additional filter functions with the output of the spikegenerator and adding the results of these convolutions to the argumentof the nonlinearity in Eq. 1.

Other models may also be used for the spatiotemporal transformationstep. Non-limiting examples of the models include the model described inPillow J W et al. 2008, dynamic gain controls, neural networks, modelsexpressed as solutions of systems of integral, differential, andordinary algebraic equations approximated in discrete time steps, whoseform and coefficients are determined by experimental data, modelsexpressed as the result of a sequence of steps consisting of linearprojections (convolution of the input with a spatiotemporal kernel), andnonlinear distortions (transformations of the resulting scalar signal bya parameterized nonlinear function, whose form and coefficients aredetermined by experimental data, models in which the spatiotemporalkernel is a sum of a small number of terms, each of which is a productof a function of the spatial variables and a function of the spatialvariables and a function of the temporal variables, determined byexperimental data, models in which these spatial and/or temporalfunctions are expressed as a linear combination of a set of basicfunctions, with the size of the set of basis function smaller than thenumber of spatial or temporal samples, with the weights determined byexperimental data, models in which the nonlinear functions are composedof one or segments, each of which is a polynomial, whose cut pointsand/or coefficients are determined by experimental data, and models thatcombine the outputs of the above models, possibly recursively, viacomputational steps such as addition, subtraction, multiplication,division, roots, powers, and transcendental functions (e.g.,exponentiation, sines, and cosines).

Spike Generation Step

In the spike generation step, the ganglion cell firing rates areconverted into patterns (also referred to as streams) of pulses,equivalent to ganglion cell spike trains. This step may be performed byan output generating module of the processing device.

In one embodiment, for each cell m, an inhomogeneous Poisson processwith instantaneous firing rate λ_(m) is created. In one embodiment, timeintervals (bins) of length Δt are used. For each neuron, the output ofthe spatiotemporal transformation, λ_(m)(t;X) as given in Eq. 1 above ismultiplied by Δt, yielding a firing probability. A random number chosenfrom a uniform distribution between 0 and 1 is chosen. If this number isless than the firing probability, a spike at the beginning of this timeinterval is generated. In one embodiment, Δt is 0.67 ms, but other binwidths may be used. This number for Δt was chosen in the standard wayfor generating a Poisson process, that is, the bin width is chosen sothat the product of the bin width and the maximum firing rate is anumber much less than 1. The choice of bin size is a compromise betweencomputational efficiency and enabling high temporal resolution and widedynamic range. The choice may be made by one of ordinary skill in theart without undue experimentation. That is, smaller bin sizes increasecomputational time, while large bin sizes blur resolution of spikepatterns.

For the spike generation step, alternative approaches can also be used,including, but not limited to, inhomogeneous gamma processes andintegrate-and-fire processes, and Hodgkin-Huxley spike generators(Izhikevich EM 2007; Izhikevich EM 2010)

The output of the encoders—the streams of pulses—are ultimatelyconverted to a format suitable for driving the transducers, for example,electrodes, ChR2 proteins, or other light-sensitive elements. Apotential problem is that the output of a given encoder may includepulse sequences where several pulses occur in rapid succession (a“burst” of spikes or spike burst or a burst of pulses or pulse burst).If a particular kind of transducer (for example, ChR2) cannot followbursts, performance of a prosthesis may be slightly degraded.

The methods of the present invention provide for elimination of thisproblem, and this method is referred to as the burst elimination step orthe correcting or modifying step. If an encoder's output contains aburst sequence, then it is replaced by an alternative in which theoccurrence of very short intervals between spikes (or pulses) isminimized. To address this, Poisson variations of the code may begenerated. To carry this out in a manner compatible with the real timerequirement of the prosthesis, the following operation may be employed:As each brief segment of the spike generator's output is generated (thatis, the output of the rescaling, spatiotemporal transformation, andspike generating step) it is inspected. Segments containing a number ofpulses greater than or equal to a defined criterion number N_(seg) arereplaced by segments in which the number of pulses is made equal toN_(seg) and are approximately equally spaced. In one embodiment withChR2, segments are of duration T_(seg)=33 ms, and the criterion numberof pulses for replacement, N_(seg), is 3. T_(seg) may be chosen betweenat or about 3 ms to 66 ms, and N_(seg) may be chosen between at or about2 to 20. As an alternative to this procedure, the burst elimination stepmay delete any pulses that occur within a window T_(win) of a previouspulse, to ensure that no more than a criterion number N_(win) of pulsesoccur within this window. Here, T_(win) may be chosen in the same manneras T_(seg) above, and N_(win) may be chosen in the same manner asN_(seg) above. The values of T_(seg), N_(seg), T_(win), and N_(win) areselected to accommodate the dynamics of the particular transducer thatis being used.

As mentioned above the problem of spike bursts can cause degradation ofthe performance of the encoder. The problem appears to occur rarely; forexample, among the 12,000 1-second long spike trains used to generatethe baby face depicted in FIG. 9, the spike correction step was neededfor approximately 1% of the pulse sequences.

Note that our encoder can produce spikes with less variability than thenormal retina, typically, because of less noise. Thus, the encoder cancarry more information about stimuli than real cells do.

Determining the Values of the Parameters for the SpatiotemporalTransformation

As mentioned in the previous section, in one embodiment, thespatiotemporal transformation is carried out via a linear-nonlinear (LN)cascade, as given in Eq. 1. This section describes one method fordetermining the parameters for L_(m) and N_(m) in that equation. First,the normal biological retina is presented with two kinds of stimuli:white noise (WN) and a natural scene movie (NS). To generate theencoders used in the data presented in FIGS. 3-9, 12, 13, and 14 thestimuli were presented for 10 min each, and ganglion cell responses wererecorded continuously through both; the data set comprised the responsesto both stimuli. The presentation may last at least about 5 min each, atleast about 10 min each, at least about 15 min each or at least about 20min each, although other time intervals may also be used. Determinationof the length of measurement time may be done by one of ordinary skillin the art without undue experimentation. The values of the parameters,L_(m) and N_(m) are then chosen to maximize the log likelihood of theobserved spike trains under the rate function of Eq. 1, where the loglikelihood, Z, is given by

$\begin{matrix}{Z = \left\langle {\sum\limits_{m}\left( {{\sum\limits_{i}{\log\left\lbrack {\lambda_{m}\left( {{\tau_{m}(i)};X} \right)} \right\rbrack}} - {\int_{t = 0}^{end}{{\lambda_{m}\left( {t;X} \right)}\ {\mathbb{d}t}}}} \right)} \right\rangle_{X}} & (2)\end{matrix}$where all terms are as defined above, and in addition, τ_(m)(i) is thetime of the ith spike in the mth cell in response to stimulus X. Notethat in Eq. 2, Z depends on L_(m) and N_(m) implicitly, because thesequantities are involved the calculation of λ_(m) via equation 1. Tomaximize the log likelihood, the following procedure may be followed.The nonlinearity N_(m) is first assumed to be exponential, since in thiscase, the log likelihood, Z, has no local maxima (Paninski et al. 2007).After optimizing the linear filters and the exponential nonlinearity(for example, by coordinate-ascent), the nonlinearity is replaced by aspline. Final model parameters are then determined by alternating stagesof maximizing the log likelihood with respect to (i) the splineparameters and (ii) the filter parameters, until a maximum is reached.

This approach can also be used for extensions of Eq 1, which may includehistory dependence and correlations among ganglion cells as in (Pillow JW et al. 2008; Nichols et al, 2010)

Alternatively, instead of using maximum likelihood, other suitableoptimization methods may be used to determine the parameters.Non-limiting examples include, optimization of a cost function, such as,the mean-squared error between the calculated rate function λ_(m) foreach stimulus X, and the measured firing rate of the mth cell inresponse to the stimulus X. Additionally, the parameter estimationprocedure can make use of other optimization methods (as alternatives togradient ascent), such as line search or simplex methods. Otheroptimization techniques may also be used (see, for example, Pun L 1969).

The use of WN and NS stimuli to find the parameters for thespatiotemporal transformations, or more generally, to find theparameters for the encoders (also referred to as the input/output modelsfor the cells), provides for a unique set of parameters as compared withthe use of a single type of stimulus (e.g. either WN or NS alone).

Developing input/output models for retinal ganglion cells, or otherretinal cells has been a long-standing difficult problem: models thatwork well for one kind of stimulus do not work well for others. Forexample, models optimized for WN stimuli do not perform optimally for NSstimuli and vice versa.

Strategies to address this problem have focused on using biologicalapproaches, whereby the model has a mechanism for adaptationincorporated into it to allow it to adapt to different image statistics.Approaches include quasi-linear models that have components thatexplicitly adapt (e.g, parameters that depend on the statistics of theinput (see, for example, Victor (1987) where the time constant of afilter was made to explicitly depend on input contrast), or nonlinearmodels in which the adaptation is an emergent property of the nonlineardynamics (see Famulare and Fairhall (2010). These strategies, however,are not practical to implement in a data-driven way for a broad range ofstimuli as needed for this invention: for the quasi-linear model, thenumber of parameters is too large for the amount of data that can beprovided in experimental retinal recordings, potentially precluding itsuse, and for the nonlinear model, even getting off the ground isdifficult, as it's not clear what functional form should be use for thedynamics (e.g., to get it to accurately capture responses to both WN andNS).

As shown in the examples throughout this document, the approach takenhere is highly effective, that is, it is able to produce a very reliablemapping of input/output relations for a broad range of stimuli,including artifical and natural stimuli. It is effective in large partbecause WN and NS are complementary. Specifically, in both the temporaland spatial domains, the NS stimuli are much more heavily weightedtowards low frequencies than the WN stimuli (and the WN stimuli are muchmore heavily weighted towards high frequencies than the NS stimuli).Their complementary nature has a major benefit. The combined stimulussets sample a diverse space of inputs that drives the optimization to adifferent location in parameter spaces than would be found by eitherstimulus set alone. The parameters are not the average of those foundusing WN and NS alone, but are a distinct set of model parameters thatdescribe the response to both stimulus sets and other stimuli (gratings,etc) as well. The latter is what makes the models generalizable; thatis, the latter is what allows the encoders to perform well on a broadrange of stimuli (including artificial and natural stimuli), i.e.,produce responses that are the same, or substantially similar, to thoseproduced by normal retinal cells when exposed to the same stimuli.

Although we have described and built the encoders in a modular fashionwith a specific set of algorithmic steps, it is evident that algorithmsor devices with substantially similar input/output relationships can bebuilt with different steps, or in a non-modular fashion, for example, bycombining any two or three of the steps in to a single computationalunit, such as an artificial neural network.

Given the encoders of the present invention, it is possible to generatedata sets, without the collection of physiological data, that can beused, for example, to develop parameters for alternate spatiotemporaltransformations, or to train a neural net, to produce identical orsimilar output using methods that are well known in the art. Theexplicit description of the encoders thus enables the development ofprosthetics, as well as other devices, such as, but not limited to,bionics (e.g., devices providing supranormal capability) and robotics(e.g., artificial vision systems).

For example, such an artificial neural network could use an input layerin which each node receives input from a pixel of the image, followed byone or more hidden layers, whose nodes receive input from the nodes ofthe input layer and/or from each other, followed by an output layer,whose nodes receive input from the nodes of the hidden layer(s). Theoutput nodes' activity corresponds to the output of the encoder(s). Totrain such a network, one could use any standard training algorithm,such as back propagation, with the training input consisting of thestimuli we used to build our encoder(s) (i.e., white noise and naturalscene movies) and the training output consisting of the output of ourencoder(s). This exemplifies that alternative methods could be developedeven without collecting further physiological data. (Duda and Hart 2001)

The parameters may be developed using various models of therelationships among the neural cells. Parameters may be developed forneuronal models where the neurons are considered independent, or inwhich they are coupled or correlated. For the coupled model, terms areadded that allow for a spike occurring in one neuron to influence theprobability of future spikes in other neurons. (Nichols et al 2010;Pillow J W et al. 2008).

Determining the Signaling Patterns to Drive Bipolar Cells to DriveGanglion Cells to Produce Normal or Near-Normal Retinal Output.

As shown above, the transducers are targeted for ganglion cells. Here, atransducer that targets bipolar cells is described. In particular, ChR2is used as an example.

Here, a method for determining the patterns of light stimulation to giveto the ChR2-expressing bipolar cells so they produce normal ganglioncell firing patterns is provided. Using the ganglion cell forinput/output relations, or the encoders for ganglion cells as describedabove, the light patterns to drive bipolar cells may be derived throughreverse engineering. Briefly, the transformations known, that is, thetransformations from image to ganglion cell output, are used to find thelight patterns that may be presented to the ChR2-expressing bipolarcells to produce that same ganglion cell output.

The method is as follows. In a multi-electrode recording experiment,arbitrary light patterns are presented to the ChR2-expressing bipolarcells, and ganglion cell responses are recorded; these data are used todetermine the transformation between the ChR2-expressing bipolar cellsand the ganglion cells. This transformation is then inverted. Theinverse transformation goes from any desired ganglion cell output backto the patterns of light to be presented the ChR2-expressing bipolarcells.

To carry this out, the spatiotemporal transformation from bipolar cellsto ganglion cells is determined according to the following equationλ_(m)(t)=N _(m)((S*L _(m))(t))  (3)where here S is the input to the ChR2-expressing bipolar cells, and Land N are the linear and nonlinear filters for the bipolar to ganglioncell transformation, and λ.is the firing rate of the ganglion cell. Toobtain the parameters L and N, we drive the ChR2-expressing bipolarcells with light patterns, record ganglion cell responses, and optimizemodel parameters as described in the section above. With the modelparameters in hand, the inputs to ChR2 needed to produce a desiredganglion cell output can be determined. Formally, this involvesinverting the transformation expressed by Eq. 3. For example, thefollowing equation may be used:

${S(t)} = {\frac{1}{{{L(0)} \cdot \Delta}\; t}\left( {{N^{- 1}\left( {\lambda(t)} \right)} - {\sum\limits_{a = 1}^{A}{{S\left( {t - {a\;\Delta\; t}} \right)}{L\left( {a\;\Delta\; t} \right)}}}} \right)}$What this equation gives is the next input, S(t), as a function of thedesired output λ(t), and the inputs delivered at prior times, S(t−aΔt).The summation over a spans the range of times for which the filterfunction L is nonzero. This inversion algorithm follows fromλ_(m() t)=N _(m)((S*L _(m))(t))by expressing the convolution as a discrete sum and carrying outstraightforward algebra.

The above equation represents a formal inversion, and to make itpractical, the choice of time step, Δt, and the number of lags, A, canbe done empirically, without undue experimentation. Note also that thenonlinearity, N, may not have a unique inverse, but this is not aproblem, since, for these purposes, one just needs a solution, not aunique solution—that is, one just needs some pattern to drive thebipolar to produce the correct output, that is, normal or near-normaloutput. One may, therefore, choose any inverse, as it will work. It isimportant to note that the ganglion cell encoders serve as theunderpinnings for this approach. The knowledge of the of input/output(stimulus/response) relationships of the ganglion cells that areprovided by the ganglion cell encoders permit the finding of the lightpatterns needed to drive the bipolar cells to produce the normalganglion cell firing patterns, that is, firing patterns that are thesame, or substantially similar, to those produced by normal retinalganglion cells to the same stimuli.

Transducer:

A transducer can receive an input signal and drive a neuron to fire orundergo a voltage change upon receiving this signal. In a preferredembodiment, the transducer targets a single cell and is, for example andwithout limitation, a light sensitive protein or an electrode targetingone cell. In other embodiments, the transducer targets a small group ofcells; a small group of cells may consist of one cell, a group of cells,or approximately 100 cells. In a preferred embodiment, a set oftransducers is used and each transducer targets a single cell or a smallgroup of cells as mentioned above. We refer to this set of transducersas a high resolution transducer. More than one transducer may betargeted to a given cell or small group of cells; for examplechannelrhodopsin-2 and halorhodopsin may be targeted to a single cell.

The transducer may drive any retinal cells to fire or undergo voltagechanges, including, but not limited to, retinal ganglion cells andretinal bipolar cells. An interface device may be used to connect theencoder and transducer.

The transducer could use any suitable mechanism, and can include,electrodes, optogenetic stimulators, thermostimulators, photo-thermalstimulators, etc. (Wells et al. 2005) In one embodiment, transducers,such as electrodes, are implanted into the patient's eye in such a wayas to stimulate retinal ganglion cells or retinal bipolar cells. Inanother embodiment, direct photo-activation, such as a photo-absorberbased system, is used for the transducer.

Other transducers are within the scope of these teachings, as well ascombinations of transducers or multiplexing of transducers. Thetransducer may be a light-responsive element, including, but not limitedto, a protein, for example a light-sensitive protein or alight-responsive chemical entity.

A light-sensitive protein that could serve as a transducer is alight-gated ion channel that is able to generate transmembrane iontransport in response to light. (Zhang et al. 2009; Lagali et al 2008).A light-sensitive protein may be responsive to visible light,ultraviolet light, or infrared light. Examples of light-sensitiveproteins include, Channelrhodopsin-1, Channelrhodopsin-2, LiGluR, ChETA,SFO (step function opsins), OptoXR (light-sensitive GPCR), VolvoxChannelrhodopsin-1, Volvox Channelrhodopsin-2 (ChR2), ChIEF, NpHr, eNpHRand combinations thereof. A light-sensitive protein or its activefragment may be used as a transducer. (European Patent Application No.19891976.)

Examples of light-sensitive chemical entities that may be used astransducers include synthetic photoisomerizable azobenzene regulated K+(SPARK), deoplarizing SPARK (D-SPARK), photoswitchable affinity labels(PALs), CNB-glutamate, MNI-glutamate, BHC-glutamate and combinationsthereof.

In one embodiment, the transducer is a light-responsive element inretinal ganglion cells. The code generated by the encoder may berepresented by bit streams (e.g., streams of zeros and ones, wherezero=no spike, and one=spike). The bit streams are then converted tostreams of light pulses (e.g., zero=no light, and one=light). Becausethe ganglion cells contain a light-responsive element (such as alight-sensitive protein, e.g., ChR2) that converts the light pulses intovoltage changes in the membrane, and because ganglion cells are spikingneurons, the light pulses lead to spike production, that is, to actionpotential production. If the pulsed light is of the appropriateintensity, e.g., in the range of 0.4-32 mW/mm², the action potentialscan follow the light pulses with almost 1-to-1 matching (as shown inExample 13). Thus the ganglion cell firing patterns follow the signalsfrom the encoders very closely.

In another embodiment, the transducer is a light-responsive element inretinal bipolar cells. In this case, the ganglion cells are being drivenindirectly: the bipolar cells are stimulated with light, they in turnsend signals directly or indirectly (e.g., through amacrine cells) tothe ganglion cells, causing them to fire. In this case, the stimulationprovided to the bipolar cells may be discrete pulses or continuouswaves. The light sensitive element, such as ChR2, when it receiveslight, causes the bipolar cells to undergo voltage changes and releaseneurotransmitters to their downstream neurons, and ultimately causingthe ganglion cells to fire.

Background firing in some cells may interfere with the light-sensitiveprotein's (for example, ChR2's) ability to follow the encoder's output.In one embodiment, in order to correct the background firing in aretinal ganglion cell, both ChR2 and halorhodopsin (or theirequivalents) could first be expressed in each cell. When activated byyellow light, halorhodopsin will hyperpolarize the cell, suppressingfiring. When the cell is meant to fire, the yellow light is turned offand blue light is presented. The blue light activates channelrhodopsin-2(ChR2), which depolarizes the cell, causing it to fire an actionpotential. Thus, the cells can be illuminated with yellow light tosuppress background firing, and the light can be switched from yellow toblue to produce firing. In another embodiment, the same strategy ofbi-directional control can apply to non-spiking cells as well—yellowlight would hyperpolarize the cell, and blue light would cause the cellsto depolarize.

In addition, as discussed above, the encoder sometimes produces a seriesof spikes in rapid successions (i.e., bursting), which a transducer,such as ChR2, may not follow well. To address this, Poisson variationsof the code may be generated. This version of the code is as meaningfulto the brain as the normal code, but are adapted to the kinetics of thetransducer. For example, the encoder may be adapted such that theresulting code does not have rapid successions, which is moreaccommodating to the kinetics of ChR2. Alternatively, variations of ChR2that follow spikes more tightly may be used. See section on SpikeGeneration above for the explicit strategy.

Vectors for Use with Light-Sensitive Elements

The gene encoding, for example, a light-sensitive protein, can beintroduced into the retinal cells via viral and non-viral vectors andmethods. Viral vectors include, but are not limited to, adenoviruses,adeno-associated viruses, retroviruses, lentiviruses, herpes viruses,vaccinia viruses, poxviruses, baculoviruses, and bovinepapillomoviruses, and recombinant viruses, such as recombinantadeno-associated virus (AAV), recombinant adenoviruses, recombinantretroviruses, recombinant poxviruses, and other known viruses in theart. (Ausubel et al 1989; Kay et al 2001; and Walther and Stein 2000;Martin et al. 2002; van Adel et al. 2003; Han et al, 2009; U.S. PatentPublication No. 20070261127), Methods for assembly of the recombinantvectors are well-known (see, e.g., Published PCT ApplicationWO2000015822 and other references cited herein).

An adeno-associated virus is one embodiment. Multiple differentserotypes have been reported, including, AAV1, AAV2, AAV3, AAV4, AAV5and AAV6. The AAV sequences employed in generating the vectors, andcapsids, and other constructs used in the present invention may beobtained from a variety of sources. For example, the sequences may beprovided by AAV type 5, AAV type 2, AAV type 1, AAV type 3, AAV type 4,AAV type 6, or other AAV serotypes or other adenoviruses, includingpresently identified human AAV types and AAV serotypes yet to beidentified. A variety of these viral serotypes and strains are availablefrom the American Type Culture Collection, Manassas, Va., or areavailable from a variety of academic or commercial sources.Alternatively, it may be desirable to synthesize sequences used inpreparing the vectors and viruses of the invention with knowntechniques; these techniques may utilize AAV sequences which arepublished and available from a variety of databases. The source of thesequences utilized in preparation of the constructs of the invention, isnot a limitation of the present invention. Similarly, the selection ofthe species and serotype of AAV that provides these sequences is withinthe skill of the artisan and does not limit the following invention. TheAAV may be self-complementary. (Koilkonda et al 2009)

The vector of the invention may be constructed and produced using thematerials and methods described herein, as well as those known to thoseof skill in the art. Such engineering methods used to construct anyembodiment of this invention are known to those with skill in molecularbiology and include genetic engineering, recombinant virus engineeringand production, and synthetic biology techniques. See, e.g., Sambrook etal, and Ausubel et al., cited above; and Published PCT ApplicationWO1996013598. Further, methods suitable for producing a rAAV cassette inan adenoviral capsid have been described in U.S. Pat. Nos. 5,856,152 and5,871,982. Methods for delivery of genes to the cells of the eye arelikewise well known to the art. See, e.g., Koilkonda et al., 2009 andU.S. Patent Publication 20100272688.

The gene may also be delivered through other non-viral methods known inthe art, including, but not limited to, plasmids, cosmids and phages,nanoparticles, polymers (e.g., polyethylenimine), electroporation,liposomes, Transit-TKO transfection reagent (Mirus Bio, Madison, USA).Cai et al. 2010; Liao et al. 2007; Turchinovich et al. 2010) A detailedreview of possible techniques for transforming genes into desired cellsof the eye is taught by Wright. (Wright 1997) It may also be possible touse encapsulated cell technology as developed by Neurotech (Lincoln,R.I., USA).

Regulatory Sequences

The vector may include appropriate expression control sequencesincluding, but not limited to, transcription initiation, termination,promoter and enhancer sequences; efficient RNA processing signals suchas splicing and polyadenylation signals; sequences that stabilizecytoplasmic mRNA; sequences that enhance translation efficiency (i.e.,Kozak consensus sequence); sequences that enhance protein stability; andwhen desired, sequences that enhance protein processing and/orsecretion. A large number of different expression control sequences,e.g., native, constitutive, inducible and/or tissue-specific, are wellknown in the art and may be utilized to drive expression of the gene,depending upon the type of expression desired. The selection of theappropriate expression sequences can be accomplished by one of ordinaryskill in the art without undue experimentation.

For eukaryotic cells, expression control sequences typically include apromoter, an enhancer, such as one derived from an immunoglobulin gene,SV40, cytomegalovirus, etc., and a polyadenylation sequence which mayinclude splice donor and acceptor sites. The polyadenylation sequencegenerally is inserted following the transgene sequences and before the3′ ITR sequence. In one embodiment, the bovine growth hormone polyA isused.

Another regulatory component of the vector useful in the methods of thepresent invention is an internal ribosome entry site (IRES). An IRESsequence, or other suitable systems may be used to produce more than onepolypeptide from a single gene transcript. An IRES (or other suitablesequence) is used to produce a protein that contains more than onepolypeptide chain or to express two different proteins from or withinthe same cell. An example of an IRES is the poliovirus internal ribosomeentry sequence, which supports transgene expression in retinal cells.

The selection of the promoter to be employed in the vector may be madefrom among a wide number of constitutive or inducible promoters that canexpress the selected transgene in an ocular cell. In one embodiment, thepromoter is cell-specific. The term “cell-specific” means that theparticular promoter selected for the recombinant vector can directexpression of the selected transgene in a particular ocular cell type.In an embodiment, the promoter is specific for expression of thetransgene in retinal ganglion cells. In an embodiment, the promoter isspecific for expression of the transgene in bipolar cells.

As discussed above, each class of retinal ganglion cells or retinalbipolar cells uses its own code. In one embodiment of the invention,only one class of ganglion cells is targeted. Expression of thelight-sensitive protein may be controlled by a cell-specific promoter.For example, the mGluR6 promoter may be employed to control expressionin ON-bipolar cells. (Ueda et al. 1997). For example, thelight-sensitive protein may be expressed in retinal ganglion cells via aganglion cell-specific gene promoter, for example, Thy-1. (Arenkiel etal 2007; Barnstable et al 1984)

In one embodiment, the transducer will be targeted to a specific classof retinal cells using a specific two vector cre-lox system describedhere (for a description of cre-lox methodology in general, see Sauer(1987). For example, ChR2, may be targeted to a subset of OFF ganglioncells as follows: In one viral vector, the inverted ChR2 gene may beflanked by loxP sites oriented in opposite directions under theregulation of the calretinin promoter; calretinin is expressed in asubset of OFF retinal ganglion cells and in some amacrine cells(Huberman et al, 2008). Then a second viral vector may be introducedthat expresses Cre recombinase under the regulation of the Thy-1(promoter, a promoter expressed in retinal ganglion cells (Barnstable etal 1984). Since the Thy 1 promoter will express the Cre recombinase onlyin ganglion cells, the inverted ChR2 will only get flipped and expressedin these cells, and not the amacrine cells. The expression of correctlyoriented ChR2 will occur only cells where both the calretinin promoterand the Thy 1 promoter are active, that is, the subset of OFF retinalganglion cells. (Note that both the Thy 1 and calretinin promoters maybe active in areas outside of the retina, but they won't causeexpression of the genes in the vectors, because the vectors are onlyapplied to the eye, specifically, the retina).

The idea can also be done in reverse (useful depending on the promoterswe have): e.g., we can use Thy1 to drive CHR2 in ganglion cells. We putit in the correct orientation and with lox sequences flanking it. Wethen use another promoter, for example, the GABA A receptor promoter, toactivate Cre recombinase in some subset of ganglion cells. The Cre willinvert the ChR2 in those cells, shutting it off—so the ChR2 will only beactive in cells that express Thy-1 and that do express the otherpromoter. It does not matter if the Cre is also activated in otherclasses, because the ChR2 isn't in them, so there's no ChR2 to turn off.

These same approaches apply to other classes of retinal ganglion cells.Their targeting can be achieved using alternate promoters in place ofthe calretinin promoter, such as the SPIG1-promoter (Yonehara et al2008, Yonehara et al 2009), the DRD4-promoter (Huberman et al 2009),promoters for neurofilament proteins (Nirenberg and Cepko, 1993), andother promoters that drive expression in subsets of ganglion cells, suchas those identified in Siegert et al. (2009). The two vector Cre-Loxsystem described here readily extends to targeting other classes ofcells as well. Promoter analysis can be used to identify promoterfunctional fragments and derivatives (McGowen at al 1998; 4:2; Booksteinet al. 1990).

In one embodiment, multiple classes of retinal neurons are targeted, anddifferent transducers, such as different ChR2 derivatives, may beexpressed in different classes of cells. The different transducers, forexample, the different ChR2 derivatives, could differ in theirproperties including excitation wavelengths. Therefore, the codes may bedelivered to specific classes of cells by presenting the codes indifferent wavelengths. For example, if we put a blue-sensitivetransducer only in OFF cells, then we can selectively drive OFF cells bydelivering in blue the light pulses produced by the OFF cell code. Theother cell classes will not respond to the blue light and thus will notbe driven by the OFF cell code.

The architecture of the ganglion cell layer (GCL) of the primate retinaalso allows for targeting of specific cell types. Ganglion cell bodieslie within the GCL. Near the fovea, the GCL is at its maximal thickness,and contains several layers of cell bodies. The cell bodies of differenttypes of cells lie in different positions within the GCL. For example,ON cell bodies lie closer to the retinal surface (closer to thevitreous) than OFF cell bodies (Perry and Silveira, 1988). Thus they canbe preferentially targeted. This can be done, for example, by low-doseinfection with a viral vector (e.g., an AAV carrying ChR2); low doseinfection will preferentially target cells closer to the surface. Thisapproach is not limited to the fovea, but can apply to any region of theretina where the GCL contains multiple sublayers.

In another embodiment, the light-responsive element may be expressed inbipolar cells. For example, an mGluR6 ChR2 plasmid (Ueda et al. 1997;U.S. Patent Publication 20090088399)) or other high efficiencyadeno-associated virus may be used to target the light-responsiveelement, for example, a gene encoding channelrhodopsin-2, to bipolarcells. (Morgans C W at al 2009; Cardin JA, et al 2010; Petrs-Silva etal. 2009; Petersen-Jones et al. 2009; Mancuso et al. 2009) Bipolarcell-specific promoters may also be used, such as promoters to glutamatereceptor genes expressed in ON bipolar cells (see Lagali et al. 2008) orpromoters for dystrophin (Fitzgerald et al. 1994). Promoter analysis canbe used to identify promoter functional fragments and derivatives(McGowen at al 1998; 4:2; Bookstein et al. 1990)

Examples of constitutive promoters which may be included in the vectorof this invention include, without limitation, the CMV immediate earlyenhancer/chicken β-actin (CβA) promoter-exon 1-intron 1 element, the RSVLTR promoter/enhancer, the SV40 promoter, the CMV promoter, the 381 byCMV immediate early gene enhancer, the dihydrofolate reductase promoter,the phosphoglycerol kinase (PGK) promoter, and the 578 by CBApromoter-exon1-intron1. (Koilkonda et al 2009). Promoter analysis can beused to identify promoter functional fragments and derivatives (McGowenat al 1998; 4:2; Bookstein et al. 1990)

Alternatively, an inducible promoter is employed to express thetransgene product, so as to control the amount and timing of the ocularcell's production. Such promoters can be useful if the gene productproves to be toxic to the cell upon excessive accumulation. Induciblepromoters include those known in the art and those discussed aboveincluding, without limitation, the zinc-inducible sheep metallothionine(MT) promoter; the dexamethasone (Dex)-inducible mouse mammary tumorvirus (MMTV) promoter; the T7 promoter; the ecdysone insect promoter;the tetracycline-repressible system; the tetracycline-inducible system;the RU486-inducible system; and the rapamycin-inducible system. Any typeof inducible promoter that is tightly regulated may be used. Other typesof inducible promoters which may be useful in this context are thosewhich are regulated by a specific physiological state, e.g.,temperature, acute phase, a particularly differentiation state of thecell, or in replicating cells only.

Selection of these and other common vector and regulatory elements areconventional and many such sequences are commercially available. See,e.g., Sambrook et al 1989 and Ausubel et al. 1989). Of course, not allvectors and expression control sequences will function equally well toexpress all of the transgenes of this invention. However, one of skillin the art may make a selection among these expression control sequenceswithout departing from the scope of this invention. Suitablepromoter/enhancer sequences may be selected by one of skill in the artusing the guidance provided by this application. Such selection is aroutine matter and is not a limitation of the molecule or construct. Forinstance, one may select one or more expression control sequences,operably link the sequence to a transgene of interest, and insert theexpression control sequence and the transgene into a vector. The vectormay be packaged into an infectious particle or virion following one ofthe methods for packaging the vector taught in the art.

The vector containing the desired light-sensitive element andcell-specific promoter for use in the target ocular cell as detailedabove is preferably assessed for contamination by conventional methodsand then formulated into a pharmaceutical composition intended forretinal injection. Such formulation involves the use of apharmaceutically and/or physiologically acceptable vehicle or carrier,particularly one suitable for intravitreal, retinal, or subretinalinjection, such as buffered saline or other buffers, e.g., HEPES, tomaintain pH at appropriate physiological levels. A variety of such knowncarriers are provided in Published PCT Application WO2002082904,incorporated herein by reference. If the virus is to be storedlong-term, it may be frozen in the presence of glycerol.

According to the method of this invention for treating an oculardisorder characterized by retinal degeneration, the pharmaceuticalcomposition described above is administered to the subject having such ablinding disease by intravitreal, retinal, or subretinal injection.Methods for the ocular administration of vectors are well known to theart. See, e.g., Koilkonda et al., 2009 and U.S. Patent Publication20100272688.

An effective amount of a vector carrying a nucleic acid sequenceencoding the desired light-sensitive element under the control of thecell-specific promoter sequence may range between about 1×10⁹ to 2×10¹²infectious units in a volume of between about 150 to about 800microliters. The infectious units are measured as described inMcLaughlin et al, 1988. More desirably, an effective amount is betweenabout 1×10¹⁰ to 2×10¹¹ infectious units in a volume of between about 250to about 500 microliters. Still other dosages in these ranges may beselected by the attending physician, taking into account the physicalstate of the subject, preferably human, being treated, the age of thesubject, the particular ocular disorder and the degree to which thedisorder, if progressive, has developed.

It may also be desirable to administer subsequent dosages of thepharmaceutical compositions of this invention. For example, dependingupon the duration of the transgene within the ocular target cell, onemay deliver booster dosages at 6 month intervals, or yearly followingthe first administration.

Such booster dosages and the need therefore can be monitored by theattending physicians, using, for example, the retinal and visualfunction tests and the visual behavior tests as described herein. Othersimilar tests may be used to determine the status of the treated subjectover time. Selection of the appropriate tests may be made by theattending physician. Still alternatively, the method of this inventionmay also involve injection of a larger volume of virus-containingsolution in a single or multiple injection to allow levels of visualfunction close to those found in normal retinas.

The code may be converted into light pulses by means of an opticalsource, such as, but not limited to, an LED array, a DLP Chip, ascanning laser beam or an LCD with appropriate sources. Interfaces forlight-sensitive elements are described more fully below.

In another embodiment, the transducers are electrodes. Through theelectrodes, the electrical pulses produced by the encoder drive theganglion cells, either directly or via bipolar cells, or a combinationthereof, to fire according to the encoded pulses. The implantedelectrode can be, but is not limited to, an electrode such as describedin U.S. Pat. Nos. 6,533,798 and 7,149,586; U.S. Patent Publication Nos.20080249588, 20090326623, and 20080221653.

Examples of vectors using AAV and light sensitive proteins that may beused in this prosthetic, are, but not limited to, sc-mGluR6-hChR2-GFP,mGluR6-hChR2-GFP, sc-smCBA-CHR2-GFP, sc-smCBA-CHR2-GFP,Flex-CBA-Chief-GFP. (Bill Hauswirth, personal communication) A morerecent vector using the L7 promoter, which is active in bipolar cells,may also be used, in for example, AAV2 or AAV2-Y444F orAAV2-Y444,500,730F. (See for example Sheridan C 2011; Published PCTapplications WO1998048027, WO2001094605, WO2002082904, WO2003047525,WO2003080648, WO2003093479, WO2003104413, WO2005080573, WO2007127428,WO2010011404)

Device:

A prosthetic device to implement the methods described herein comprisesthe following elements, which may be interconnected physically,wirelessly, optically, or by other means known in the art.

(1) Camera

The camera acquires images with high fidelity. In one embodiment, thecamera is based around a charge-coupled device (CCD), such as Point GreyFirefly MV (capable of 752×480 pixels, 8 bits/pixel, at 60 frames persecond) (Point Grey Research, Richmond, BC, Canada). Transmitting imagesfrom the camera to the processing device in real-time requires a highbandwidth connection. For example, a data transfer of greater than 20MB/sec can be achieved using a USB 2.0 interface between the camera andprocessing device.

The camera can be replaced by any device that can capture visual imageswith high spatial and temporal resolution, and then transfer theseimages to the processing device. These devices include, but are notlimited to, devices based on charge-coupled devices (CCDs); active pixelsensors (APS) such as complimentary metal-oxide-semiconductor (CMOS)sensors, thin-film transistors (TFTs), arrays of photodiodes; and thecombinations thereof.

The camera can be interfaced with the processing device using anyconnection capable of high speed data transfer, including, but notlimited to, serial interfaces, such as IEEE 1394 or USB 2.0; parallelinterfaces; analog interfaces, such as NTSC or PAL; a wirelessinterface; the camera could be integrated onto the same board as theprocessing device.

(2) Processing Device

The processing device implements the encoders which performs theconversion from images to the code in real-time.

The processing device, e.g., hand-held computer, can be implementedusing any device capable of receiving a stream of images andtransforming them into output in real-time. This includes, but is notlimited to, a combination general purpose processor (GPP)/digital signalprocessor (DSP); a standard personal computer, or a portable computersuch as a laptop; a graphical processing unit (GPU); afield-programmable gate array (FPGA) (or a field-programmable analogarray (FPAA), if the input signals are analog); an application-specificintegrated circuit (ASIC) (if an update is needed, the ASIC chip wouldneed to be replaced); an application-specific standard product (ASSP); astand-alone DSP; a stand-alone GPP; and the combinations thereof.

In one embodiment, the processing device is a hand-held computer(Beagleboard, Texas Instruments, Dallas, Tex.), based around a dual-coreprocessor that integrates a general purpose processor (GPP) and adigital signal processor (DSP) onto a single chip. This platform iscapable of highly-parallel computation and requires much less power thana typical portable computer (˜2 Watts or less, compared to 26 Watts fora standard laptop computer). This allows the transformation to becomputed in real-time, on a device that is portable and can be poweredon a single battery for long periods of time. For example, typicallaptop batteries, with charge capacities in the range of 40-60Watt-hours, could run the processor continuously for about 20-30 hours.In another embodiment, the processing device is small in size so that itcan be attached to eye glasses worn by a patient.

For a given location in space, the transformations specified by theencoders are applied to the series of input images, producing encodedoutput to drive the targeted cell at the desired location in space. Inone embodiment, where the targeted cells are retinal ganglion cells, theoutput of the encoders is a train of electronic pulses that specify thetime at which the retinal ganglion cell should fire. The time of eachpulse is calculated with sub-millisecond resolution. The majority of thecomputation takes place on the DSP, while the GPP is used to direct theimage data from the camera to the processor's memory, and to synchronizethe camera and DSP.

In one embodiment, where the targeted cells are retinal ganglion cells,the output of the processing device is formatted as follows: for a giventime t, the output is a matrix of bits where the element at position(x,y) corresponds to the state of ganglion cell at position (x,y): it is1 if the cell should fire a spike at time t, 0 if the cell should notfire a spike at time t. The dimensions of this matrix are sized suchthat they match the number of ganglion cells that can be stimulated. Theoutput of the encoders is then stored in memory and converted to signalsto drive the transducers via an output interface (see the descriptionunder the subheading “(4) Output Interfaces” below). The conversionoccurs in blocks. In one embodiment, the output of the encoder is storedfor 16.66 ms and then converted as a block. Blocks ranging from 5 ms to66.66 ms may be used, where the minimum block length in time isdetermined by the time delay between stimulus onset and ganglion cellfirst spike.

(3) Transducer

The transducer receives signals from the device, via the outputinterface, and activates the targeted cells as specified by theencoders. The transducer is detailed above in the section “Transducer.”

(4) Output Interfaces

The output interface translates the encoded output (from the processingdevice) into a form that can drive the transducer. Several outputinterfaces are possible, depending on the transducer that has beenchosen. For example, if the retinal ganglion cell encoders are pairedwith a light-sensitive transducer (such as ChR2) that is expressed inretinal ganglion cells, the output interface may be a digital lightprocessing (DLP) device. This DLP device would output pulses of lightthat correspond to the encoded ganglion cell output it receives from theencoder device. The pulses of light would then drive the transducer inthe ganglion cells, causing the ganglion cells to fire as the encoderspecifies. In this example, the output interface functions as follows:the output of the encoders is sent from the processing unit to theoutput interface (DLP). The output interface then converts the binarydata, which represents action potential times, into light pulses, usinga digital micromirror device (DMD) that is paired with a high intensitylight emitting diode (LED). The DMD is a grid of mirrors whose positioncan be switched with high temporal and spatial resolution. When theencoders dictate that the ganglion cell at position (x,y) should fire anaction potential, the mirror at position (x,y) on the device is switchedto the “on” position for a brief period (e.g., millisecond-timescale),and then switched back to the “off” position. This reflects light fromthe LED onto the retina for a brief period, causing a light pulse atposition (x,y). This light pulse drives the retinal ganglion cell atposition (x,y) to fire.

In one embodiment, the device is paired with the light-sensitivetransducer ChR2, expressed in retinal ganglion cells, and the outputinterface is a digital light processing (DLP) device as described above(TI DLP Pico Projector Development Kit v2.0, Texas Instruments, Dallas,Tex.). The standard light source on the DLP device may be replaced witha high intensity LED, intense enough to activate ChR2 (Cree XP-E BlueLED, Cree, Durham N.C.). As mentioned above, the DLP contains a digitalmicromirror device (DMD) (DLP1700A, Texas Instruments, Dallas, Tex.),which consists of a grid of mirrors, each of which can be switched toreflect the light from the LED onto the retina when the retinal ganglioncell at that location should fire. Data is sent from the encoding deviceto the output interface over a High Definition Multimedia Interface(HDMI, 22 MB/sec). The position of each mirror on the DMD is controlledwith high temporal resolution—when an encoder dictates that a ganglioncell should fire an action potential, the mirror at the correspondinglocation is switched to the “on” position for a brief time period (1.4ms). The mirror switching states causes the device to output a pulse oflight to the corresponding location, which drives the targeted retinalganglion cell to fire an action potential. The mirror switching time maybe shorter or longer, for example from 0.1 ms to 10 ms, depending on theamount of light required to activate the cell. In this embodiment, thearray of mirrors on the DMD is 480 by 320 mirrors, and is thus capableof targeting over 150,000 locations (e.g., cells) independently. The DLPcould also have more mirrors, e.g. 1024 by 768 mirrors, as in the caseof the DLP5500A (Texas Instruments, Dallas, Tex.), and thus couldstimulate many more locations independently. Data transfer between theencoding device and the interface follows standard specifications, aslaid out in Texas Instruments Application Report DLPA021—January2010—“Using the DLP Pico 2.0 Kit for Structured Light Applications”.

The DLP is one example of a potential output interface. The outputinterface could also be implemented using any device capable ofactivating the transducer it is paired with. For light-activatedtransducers, this includes, but is not limited to, Digital micromirrordevices; LED arrays; Spatial light modulators; Fiber optics; Lasers;Xenon lamps; Scanning mirrors; Liquid-crystal displays (LCDs), and thecombinations thereof. (Golan L, et al 2009; Grossman N et al., 2010)

For transducers based on electrodes, the output interface could consistof any device capable of driving current into the electrodes, which areknown in the art.

(5) One or more or any part thereof of the techniques described herein,including the encoder (which may include preprocessing, spatiotemporaltransformation, spike generation, and burst elimination steps) andoptimization of parameters for the encoder, can be implemented incomputer hardware or software, or a combination of both. The methods canbe implemented in computer programs using standard programmingtechniques following the method and figures described herein. Programcode is applied to input data to perform the functions described hereinand generate output information. The output information is applied toone or more output devices such as a display monitor. Each program maybe implemented in a high level procedural or object oriented programminglanguage to communicate with a computer system. However, the programscan be implemented in assembly or machine language, if desired. In anycase, the language can be a compiled or interpreted language. Moreover,the program can run on dedicated integrated circuits preprogrammed forthat purpose.

Each such computer program is preferably stored on a storage medium ordevice (e.g., ROM or magnetic diskette) readable by a general or specialpurpose programmable computer, for configuring and operating thecomputer when the storage media or device is read by the computer toperform the procedures described herein. The computer program can alsoreside in cache or main memory during program execution. The analysis,preprocessing, and other methods described herein can also beimplemented as a computer-readable storage medium, configured with acomputer program, where the storage medium so configured causes acomputer to operate in a specific and predefined manner to perform thefunctions described herein. In some embodiments, the computer readablemedia is tangible and substantially non-transitory in nature, e.g., suchthat the recorded information is recorded in a form other than solely asa propagating signal.

In some embodiments, a program product may include a signal bearingmedium. The signal bearing medium may include one or more instructionsthat, when executed by, for example, a processor, may provide thefunctionality described above. In some implementations, signal bearingmedium may encompass a computer-readable medium, such as, but notlimited to, a hard disk drive, a Compact Disc (CD), a Digital Video Disk(DVD), a digital tape, memory, etc. In some implementations, the signalbearing medium may encompass a recordable medium, such as, but notlimited to, memory, read/write (R/W) CDs, R/W DVDs, etc. In someimplementations, signal bearing medium may encompass a communicationsmedium such as, but not limited to, a digital and/or an analogcommunication medium (e.g., a fiber optic cable, a waveguide, a wiredcommunications link, a wireless communication link, etc.). Thus, forexample, the program product may be conveyed by an RF signal bearingmedium, where the signal bearing medium is conveyed by a wirelesscommunications medium (e.g., a wireless communications medium conformingto the IEEE 802.11 standard).

It is to be understood that any of the signals and signal processingtechniques may be optical or digital or analog in nature, orcombinations thereof.

As mentioned above, the output of the encoders is stored in blocks forconversion to signals to drive the transducers (via the outputinterface). For example, in one embodiment, where the output interfaceproduces light pulses using a DLP, the output of the encoders istranslated into signals to control the states of the mirrors in the DLP(either reflect toward the retina or reflect away from the retina). Theconversions are performed in blocks. In one embodiment, the output ofthe encoders is stored for 16.66 ms and converted as a block. Blocksranging from 5 ms to 66.66 ms may be used, where the minimum blocklength in time is chosen to correspond to the minimum time delay betweenstimulus onset and ganglion cell first response (in normal WT retinas).An additional advantage of the block storage is that it allows for theburst elimination step described in the section entitled, “SpikeGeneration Step” under the section entitled, “Encoders” to be performed.

Methods to Measure Performance of the Encoder and the Prosthetic

The following describes the procedure for measuring the performance ofthe encoder and the prosthetic. Performance can be measured in at leastthree different ways: by performance on a forced choice visualdiscrimination task, or accuracy on a Bayesian stimulus reconstructiontest, or performance on an error pattern test. The term “test stimulus”that will be used herein, refers to a stimulus or a stimuli, which ispresented to an animal for evaluation of performance of the encoders orencoders+transducers (i.e., the retinal prosthetic). The term “stimulusreconstructed” that will be used herein, refers to a reconstruction ofthe stimulus using methods described herein. The term “activated retina”refers to a retina treated with encoders+transducers; this includestransducers targeted to ganglion cells or bipolar cells.

It is important that the task used to measure prosthetic performancefalls into a range of difficulty that allows meaningful information tobe obtained, as the task used in Example 8 shows. Briefly, the task mustbe difficult enough (i.e. must use a stimulus set rich enough) that thenormal retinal responses provide information about the stimuli, but donot perform perfectly on the task. For example, in the task shown in theexample, the fraction correct using the responses from the normalretina, was 80%, satisfying this criterion. If the task used is toohard, such that the normal retina's performance is near chance, thenmatching is of limited use to a performance analysis. Conversely, if thetask chosen is too easy (e.g., requiring just gross discriminations,such as black versus white, and where the fraction correct for theresponses from the normal retina is near 100%), then prosthetic methodsthat are far from approximating the retina's natural code and providenothing close to normal vision could appear to do well. Thus, it iscritical to use an appropriately challenging test, as was used in theaccompanying examples. The use of a challenging test also allows one todetermine if the prosthesis is performing better than the retina (i.e.,entering into the domain of “bionic vision”).

To evaluate performance on a forced choice visual discrimination task, aknown test in the art, a confusion matrix is used (Hand DJ. 1981). Aconfusion matrix shows the probability that a response to a presentedstimulus will be decoded as that stimulus. The vertical axis of thematrix gives the presented stimulus (i), and the horizontal axis givesthe decoded stimulus (j). The matrix element at position (i,j) gives theprobability that stimulus i is decoded as stimulus j. If j=i, thestimulus is decoded correctly, otherwise, the stimulus is decodedincorrectly. Put simply, elements on the diagonal indicate correctdecoding; elements off the diagonal indicate confusion.

In this task, an array of stimuli is presented, specifically, stimulicontaining natural scenes (see below for requirement for stimuli forthis task), and the extent to which the stimuli can be distinguishedfrom each other, based on the responses of the ganglion cells and/orencoders, is measured. For the data generated in FIG. 8, which is usedto set the criterion for performance on the discrimination taskdescribed here, the responses of the ganglion cells were recorded with amulti-electrode array as in Pandarinath et al, 2010, and the stimuliwere presented on a computer monitor.

A training set is obtained in order to build response distributions (the“training set”), and another set is obtained to be decoded to calculatethe confusion matrix (the “test set”).

To decode the responses in the test set, one determines which of thestimuli s_(j) was the most likely to produce it. That is, one determinesthe stimulus s_(j) for which p(r|s_(j)) was maximal. Bayes theorem isused, which states that p(s_(j)|r)=p(r|s_(j))p(s_(j))/p(r), wherep(s_(j)|r) is the probability that the stimulus s_(j) was present, givena particular response r; p(r|s_(j)) is the probability of obtaining aparticular response r given the stimulus s_(j); and p(s_(j)) is theprobability that the stimulus s_(j) was present. p(s_(j)) is set equalfor all stimuli in this experiment and so, by Bayes Theorem, p(s|r_(j))is maximized when p(r|s_(j)) is maximized. When p(s_(j)) is uniform, asit is here, this method of finding the most likely stimulus given aresponse is referred to as maximum likelihood decoding (Kass et al.2005; Pandarinath et al. 2010; Jacobs et al. 2009). For eachpresentation of stimulus s_(i) that resulted in a response r that wasdecoded as the stimulus s_(j), the entry at position (i,j) in theconfusion matrix is incremented.

To build the response distributions needed for the decoding calculationsused to make the confusion matrices (i.e., to specify p(r|s_(j)) for anyresponse r), the procedure is as follows. The response r was taken to bethe spike train spanning 1.33 sec after stimulus onset and binned with66.7 ms bins, as in the examples in this document where confusionmatrices were generated. The spike generation process is assumed to bean inhomogeneous Poisson process, and the probability p(r|s_(j)) for theentire 1.33 s response is calculated as the product of the probabilitiesfor each 66.7 ms bin. The probability assigned to each bin is determinedby Poisson statistics, based on the average training set response inthis bin to the stimulus s_(j). Specifically, if the number of spikes ofthe response r in this bin is n, and the average number of spikes in thetraining set responses in this bin is h, then the probability assignedto this bin is (h^(n)/n!)exp(−h). The product of these probabilities,one for each bin, specifies the response distributions for the decodingcalculations used to make the confusion matrices.

Once the confusion matrices are calculated, overall performance in theforced choice visual discrimination task is quantified by “fractioncorrect”, which is the fraction of times over the whole task that thedecoded responses correctly identified the stimuli. The fraction correctis the mean of the diagonal of the confusion matrix.

Given this procedure, 4 sets of analyses are performed. For each one,the responses from the WT retina are used for the training set and adifferent set of responses is used for the test set, as outlined below:

(1) The first set should consist of responses from the WT retina. Thisis done to obtain the fraction correct produced by normal ganglion cellresponses.

(2) The second set should consist of the responses from the encoders(the responses from the encoders, as indicated throughout this document,are streams of electrical pulses, in this case, spanning 1.33 sec afterstimulus presentation, and binned with 66.7 ms, as are the WT ganglioncell responses). Responses from this test set yield a measure of howwell the encoders perform, given the response distributions of thenormal WT retina. The basis for this is that the brain is built tointerpret the responses of the normal WT retina (i.e., the naturallyencoded responses.) When responses from the encoder are used as a testset, one obtains a measure of how well the brain would do with our proxyof the normal retinal responses (our proxy of the retina's code).

(3) The third set should consist of responses from a retina of a blindanimal driven by the encoders+transducers (ChR2), where the responsesare of the same duration and bin size as above. This set provides ameasure of how well the encoder performs after its output has beenpassed through the transducer in real tissue.

(4) Finally, the last set consists of the responses from a retina of ablind animal driven by just the transducer (ChR2), with responses of thesame duration and bin size as above. This gives us a measure of how wellthe standard optogenetic method performs. This is essentially a controlexperiment to show that the discrimination task provides an adequatetest, as explained in the paragraph above concerning appropriatedifficulty of the test.

As shown in Example 8, the encoder's performance in the forced choicevisual discrimination task was 98.75% of the normal retina'sperformance, the complete system's performance, that is, the performanceof the current embodiment of the encoder+transducer, was 80% of thenormal retina's performance, and the performance of the standard method(just transducer alone) was less than 10% of the normal retina'sperformance (8.75%). Thus, when tested in vitro or in an animal model,the performance of the prosthesis in the forced choice visualdiscrimination task, as measured by “fraction correct”, will be at leastabout 35%, 50%, 60%, 70%, 80%, 90%, 95%, 99%, or 100% of the performanceof the normal retina, or better than the normal retina, measured asdescribed above. Note that 35% is about 4 times better than theperformance of the optogenetic approach in Example 8. Likewise, theperformance of the encoder by itself, because it can be used inconjunction with other transducers or for other purposes, such as butnot limited to robot vision, will be at least about 35%, 50%, 60%, 70%,80%, 90%, 95%, 99%, or 100% of the performance of the normal retina, orbetter than the normal retina, measured as described above.

The performance of the encoder may also be measured using stimulusreconstruction. Stimulus reconstruction uses a standard maximumlikelihood approach to determine the most likely stimulus presentedgiven a set of spike trains (reviewed in Paninski, Pillow, and Lewi,2007). While the brain does not reconstruct stimuli, reconstructionsserve as a convenient way to compare methods and give an approximationof the level of visual restoration possible with each approach.

The stimulus should be a uniform gray screen for 1 second, followed by agiven image for 1 second, preferably a human face. Each pixel of thestimulus must span a reasonable region of visual space, so that featuresof the image, in this case a face can be discerned. This criterion issatisfied by a choice of 35 by 35 pixels per face, as shown in FIG. 9.This is consistent with the fact that facial recognition makes use ofspatial frequencies at least as high as 8 cycles per face, whichrequires at least 32 pixels in each dimension for adequate sampling(Rolls et al, 1985). In the example shown in FIG. 9, which uses mouse,each pixel corresponded to 2.6 degrees by 2.6 degrees of visual space.This in turn corresponds to approximately 12-20 ganglion cells on themouse retina.

Reconstructing the stimulus consists of a search over the space of allpossible stimuli to find the most likely stimulus given the measuredpopulation response r. To find the most likely stimulus given r, Bayes'theorem, p(s|r)=p(r|s)*p(s)/p(r) used. Because the a priori stimulusprobability p(s) is assumed to be constant for all s, maximizing p(s|r)is equivalent to maximizing p(r|s).

To determine p(r|s), it is assumed that the cells' responses areconditionally independent that is, it is assumed that p(r|s) is theproduct of the probabilities p(r_(j)|s), where p(r_(j)|s) is theprobability that the jth cell's response is r_(j), given the stimulus s.The rationale for this assumption is that it has been shown thatdeviations from conditional independence are small, and contribute onlya small amount to the information carried (Nirenberg et al, 2001; Jacobset al, 2009) and to the fidelity of stimulus decoding.

To calculate p(r_(m)|s) for a given cell m, the response r_(m) is takento be the spike train of the mth cell spanning 1 sec after stimulusonset and binned with 0.67 ms bins. Since the spike generation processis assumed to be an inhomogeneous Poisson process, the probabilityp(r_(m)|s) for the entire 1 sec response is calculated as the product ofthe probabilities assigned to each bin. The probability assigned to eachbin is determined by Poisson statistics based on the cell's expectedfiring rate in this bin to the stimulus s. The cell's expected firingrate is calculated from Eq. 1 (see section “The Encoders,” under“Spatiotemporal Transformation Step”), as the quantity λ_(m)(t;X), whereX in eq. 1 is taken to be the stimulus s, and t is the time of the bin.Finally, the probability of the response for the population of cells,p(r|s), is calculated by multiplying the probabilities of the responsesof the individual cells p(r_(j)|s).

To find the most likely stimulus s_(j) for the population response, r,standard gradient ascent techniques are used. The goal is to find thestimulus s_(j) that maximizes the probability distribution p(r|s). Sincethe stimulus space is high-dimensional, the gradient ascent method isused as it provides an efficient way to search through thishigh-dimensional space. The procedure is as follows. The search startsat a random point in stimulus space, s_(k). The probability distributionp(r|s_(k)) for this stimulus is evaluated, and the slope of thisprobability distribution with respect to each dimension of the stimulusis calculated. A new stimulus s_(k+1), is then created by changing thestimulus s_(k) in the direction of increasing probability (as determinedfrom the slope of the probability distribution). This process iscontinued iteratively until the probability of the stimulus starts toincrease by only a marginal amount, i.e., until the peak of p(r|s) isreached. Note that because the probability distribution is not strictlylog-concave, there exists the possibility of getting stuck in localmaxima. To verify that this is not occurring, reconstructions usingmultiple random starting points must be performed to confirm that theyconverge to the same peak.

To compare the performance of the prosthetic methods, reconstructionsmust be performed from 3 sets of responses: 1) responses from theencoders, 2) responses from a blind retina, where the ganglion cells aredriven by the encoders+transducers (ChR2), and 3) responses from a blindretina, where the ganglion cells were driven by just the transducers(i.e., just ChR2). The reconstructions should be carried out onprocessing clusters in blocks of 10×10 or 7×7 pixels, so as to makecomparisons to the results in the Examples (FIG. 9 specifically).

To obtain a large enough dataset for the complete reconstruction, it maybe necessary to move the image systematically across the region ofretina one is recording from, so that responses to all parts of theimage can be obtained with a single or small number of retinas.Approximately 12,000 ganglion cell responses were recorded for eachimage in FIG. 9. The performance should be the same or substantiallysimilar to that shown in FIG. 9B. Not only is it possible to tell thatthe image is a baby's face, but one can also tell that it is thisparticular baby's face, a particularly challenging task.

To quantify the differences in the performance of the methods, eachmethod's reconstruction must be compared with the original image. Thisis done by calculating the standard Pearson correlation coefficientbetween the reconstructed image's values at each pixel, and that of thereal image. With this measure, a correlation coefficient of 1 indicatesthat all of the original image's information was perfectly retained,while a correlation coefficient of 0 indicates that the resemblance ofthe reconstruction to the real image was no greater than chance.

As shown in FIG. 9, the results were as follows: for the encoders alone,the correlation coefficient was 0.897; for the encoders plustransducers, the correlation coefficient was 0.762, and for thetransducers alone (corresponding to the current art), the correlationcoefficient was 0.159. Thus, just as we found for the discriminationtask, the performance of the encoders+transducers was several-foldbetter than the performance of the current art.

Thus, when tested in vitro or in an animal model, the performance of theprosthesis, as measured by reconstruction accuracy may be as follows:The Pearson's correlation coefficient between the reconstruction fromthe responses of the encoders+transducers (the retinal prosthetic) andthe original image will be at least about 0.35, 0.50, 0.60, 0.70, 0.80,0.90, 0.95, or 1.0. Likewise, the Pearson's correlation coefficientbetween the reconstruction from the encoder's responses and the originalimage, will be at least about 0.35, 0.50, 0.60, 0.70, 0.80, 0.90, 0.95,or 1.0, or will perform better than the normal retina, measured asdescribed above. Note that 0.35 is >2 times better than the performanceof the optogenetic method in Example 8.

An additional test that can be performed on the confusion matrix data isa test that focuses on the pattern of errors, the “Error Pattern Test,”which is measured using a standard measure in the art, the mean squarederror (MSE). To test the effectiveness of the encoders and theencoders+transducers (i.e., the prosthetic method), the error pattern isevaluated for sets (2), (3), and (4) above, since this quantity iscalculated with reference to the set (1). The extent to which the errorpattern for each set ((2), (3), or (4)) matches that of the WT (i.e.,the normal) (set (1)) is quantified by the mean-squared error (MSE),which is defined as the average of the square of the difference betweenthe elements of the confusion matrix determined for one of the test sets((2), (3), or (4)), and the WT (set (1)). The rationale for this test isthat the pattern of decoding errors indicate which stimuli are likely tobe confused by the brain when it receives the retinal output, i.e.,which stimuli cannot be distinguished from each other. As can be seen inExample 8, the normal (WT) retina has a range of performance—there aresome stimuli that can be readily distinguished by the responses of thereal cells, and some that cannot. For example, as shown in the top rightconfusion matrix of FIG. 8 in Example 8, the responses of the populationof WT ganglion cells are clearly able to distinguish 10 of the 15stimuli presented (indicated by the 10 bright squares along the diagonalof the matrix); in contrast, the responses of the population of WTganglion cells show confusion for the remaining 5 stimuli (as indicatedby the presence of off-diagonal squares). The Error Pattern Testprovides a way to quantify the extent to which the responses of theencoders, the encoders+transducers, and the transducers alone,distinguish or confuse the same stimuli. It measures the extent to whichthe confusion matrices for sets (2), (3), and (4) match that of set (1);specifically, it calculates the average of the square of the differencebetween the elements of the test confusion matrices (sets (2), (3), and(4)) and the WT (set (1)). To develop a retinal prosthetic that providesnormal or near-normal vision, it is necessary that the neural signalsbeing sent to the brain (i.e., the ganglion cell firing patterns)provide the same information that normal cells provide, that is, thatstimuli that are normally distinguished are distinguished, and stimulithat are normally perceived as similar remain that way (are perceived assuch when the prosthetic is used).

When the data from Example 8 was used to measure the error pattern, theresults were the following: the encoder's performance yielded an MSE of0.005; that is, the match to the error pattern of the normal retina wasvery close. The complete system's performance (encoders+transducers)yielded an MSE of 0.013, also very close. The transducer alone yieldedan MSE of 0.083, a much higher value, indicating that the match to thenormal error pattern was poor. Thus, when tested in vitro or in ananimal model, the match to the error pattern of the real retina, asmeasured by MSE, may be at most about 0.04, 0.03, 0.02, 0.01, or 0.005.Note that 0.04 indicates a match that is at least twice as good (since0.04 is less than half of 0.083) as the optogenetic approach in Example8, and the encoder+transducer yields a match of 0.013, substantiallybetter than that.

In order to test a prosthetic using the methods described herein,mammalian retinas with transducers applied to the same retinal cellclasses are obtained, as are wild type retinas of the same species. Thetests described above are then executed. For all the analyses above, theresults should be consistent across retinas of the same type, forexample at least about five retinas.

Measures of Clinical Utility

Visual Acuity.

The World Health Organization (WHO) defines low vision as best correcteddistant visual acuity in the better eye less than 20/60 but 20/400 orbetter, or widest diameter of the visual field subtending an angle ofless than 20 degrees but greater than 10 degrees, and blindness as bestcorrected distant visual acuity in the better eye of less than 20/400 orless or widest diameter of the visual field subtending an angle of lessthan 10 degrees. In the United States, legal blindness is defined asbest corrected distant visual acuity of 20/200 or less in the better eyeor widest diameter of visual field subtending less than 20 degrees. MostNorth American states require best corrected visual acuity with botheyes of 20/40 for an unrestricted driving license. (Riordan-Eva 2010)

Since the early 1980's the standard measure of visual acuity forclinical trials has been the Early Treatment of Diabetic RetinopathyStudy (ETDRS) chart, which has five letters on each row and spacingbetween letters and rows equal to the letter size, with a geometricprogression of letter sizes. (Kniestedt and Stamper, 2003; (Ferris F Let al 1982; ETDRS report number 7). An electronic equivalent test hasbeen developed and validated and is now widely used, known as theelectronic visual acuity test (“EVA”) (Beck R W et al 2003; Cotter S A,et al 2003).

Protocols for testing visual acuity are known in the art. A standardprotocol using ETDRS chart is as follows.

A. Visual Acuity Chart: Modified Bailey-Lovie

The ETDRS visual acuity charts 1 and 2 are used for standardizedmeasurement of visual acuity. Acuity testing of all subjects, regardlessof visual acuity, begins at four meters. Two ETDRS Visual Acuity Chartsare used for the measurement of visual acuity, each with a differentletter sequence. The right eye will always be tested with Chart 1 andthe left eye with Chart 2.

B. Illumination of Visual Acuity Charts and Room

Each clinic must have/use an ETDRS light box for the ETDRS visual acuitycharts during any study acuity testing if the EVA is non-functional. Thelight box should be hung on the wall or placed on a stand (that can bepurchased from the Lighthouse for the Blind in New York) at a heightsuch that the top of the 3rd row of letters (0.8 Log MAR) is 49+2 inches(124.5+5.1 cm) from the floor. Room lighting should be approximately 50foot-candles and should be uniform between the subject and the lightbox. The distance from the center of the exam chair to the Visual AcuityChart should be 4.0 meters.

C. Best-Corrected Visual Acuity Measurements

The right eye is tested first and then the left eye. The subject isseated such that the distance from the center of the exam chair to theETDRS Visual Acuity Chart is 4.0 meters. This testing distance is alwaysused first even if the subject could not be refracted at four meters. Inaddition to the occluder in the trial frame, the left eye is occludedwith an eye patch or pad placed beneath the trial frames. With the lenscorrection obtained by subjective refraction in the trial frame, thesubject is asked to read ETDRS Visual Acuity Chart 1 from the top withthe right eye. It is emphasized to the subject that each answer will bescored so adequate time should be allowed for each letter in order toachieve the best identification. The subject is instructed that all ofthe figures to be read are letters and that there are no numbers.

The examiner records each letter identified correctly by the subject ashe/she reads the chart by circling the corresponding letter on the ETDRSscore sheet (or study form). Letters read incorrectly, or for which noguesses are made, are not marked on this form. Each letter readcorrectly is scored as one point. The score for each line (includingzero if no letters were read correctly on that line) and the total scorefor the eye are recorded on the form, as soon as the four meter testinghas been completed.

If the number of letters read correctly at four meters is less thantwenty, the test should be repeated at one meter and both the four-meterand one-meter totals should be recorded on the ETDRS score sheet (orstudy form). Both eyes should be tested at four meters before thesubject is moved up to the one-meter test distance. It is stronglyadvised that the total number of letters correctly read at four metersbe calculated as soon as the four meter testing has been concluded inorder to identify subjects who require 1 meter testing. Prior to actualtesting at one-meter, +0.75 D sphere should be added to the correctionalready in the trial frame to compensate for the new distance. Thesubject must sit for testing at the one-meter distance.

The same procedure for obtaining visual acuity for the right eye is usedfor the left eye, except that ETDRS Visual Acuity Chart 2 is used. Chart1 should never be exposed to the left eye and chart 2 should never beexposed to the right eye, even when switching charts and occlusion.

Poor Vision Testing (Testing for Light Perception)

If the subject cannot identify any letters on visual acuity testing ofan eye (i.e., letter score=0), the eye is tested for light perceptionwith the indirect ophthalmoscope as the light source. The testingprocedure can be performed according to the investigator's usualroutine. The following procedure is indicated:

Room lighting should remain at the level of normal visual acuitytesting. The trial frame should be removed, and the subject should closethe opposite eye and occlude it by making a tight seal with the palmaround the orbit and the bridge of the nose. The indirect ophthalmoscopelight should be in focus at three feet, and the rheostat set at sixvolts. From a distance of three feet the beam should be directed in andout of the eye at least four times; the subject should be asked torespond when he/she sees the light. If the examiner is convinced thatthe subject perceives the light, vision should be recorded as lightperception, otherwise as no light perception.

Calculating the Visual Acuity Score

After each measurement of visual acuity, the visual acuity score for thevisit is calculated. The visual acuity score is defined by the number ofletters read correctly, as follows:

-   -   If twenty or more letters are read correctly at the four-meter        test distance, the visual acuity score is equal to the number of        letters (N) read correctly at four meters+30. If one or more but        less than twenty letters are read correctly at four-meter        distance, the visual acuity score is equal to the number of        letters read correctly at four meters plus the number of letters        read correctly at one meter in the first six lines.    -   If no letters are read correctly at either the four-meter        distance or the one-meter distance, the visual acuity score is        0, and testing for light perception should be performed as        described below.

Visual acuity using the ETDRS chart is scored as follows, separately foreach eye, with testing at 4 meters:

Line Acuity Letters correct 1 (top) 20/200 2 20/160 3 20/125 4 20/100 520/80 6 20/63 7 20/50 8 20/40 9 20/32 10  20/25 11  20/20 12  20/16 13 20/12.5 14  20/10 total letters

If the total number correct is 20 or more, the score is the total numbercorrect plus 30. If the total number correct is less than 20 than thepatient is tested on same chart at 1 meter and the score is recorded.

Line Acuity Letters correct 1 (top) 20/800 2 20/640 3 20/500 4 20/400 520/320 6 20/250 total correct

The visual acuity letter score is then equal to the total number ofletters read correctly at 4.0 meters, plus the total number of lettersread correctly at 1.0 meter in the first six lines.

The measures of visual acuity, (e.g. “20/20”) may also be expressed aspercentages of normal visual acuity if 20/20 is taken as normal vision,as per the following table:

PERCENTAGE OF VISUAL ACUITY EFFICIENCY 20/20 100% 20/25 96% 20/30 91%20/35 87% 20/40 84% 20/45 80% 20/50 76% 20/60 70% 20/70 64% 20/80 58%20/90 53%  20/100 49%  20/110 45%  20/120 41%  20/140 34%  20/160 29% 20/200 20%  20/240 13%  20/320 7%  20/400 5%  20/480 2%  20/800 1%<20/800 0%

Effectiveness of treatment may therefore be expressed as increased inthe number of letters read, which is easily translated to the number oflines gained in the EVA test or on the ETDRS chart, or effectiveness canbe expressed as achieving a given percentage of normal vision.

For example, treatment with the device will increase visual acuity atleast by 15 letters, on the ETDRS chart or EVA test. 15 lettersrepresents 3 lines on they ETDRS chart. If a patient presents with lowvision of 20/100, treatment with the method will improve the patient'svision to 20/50 vision, which is 76% of normal vision, or near-normalvision.

Treatment with the device will increase visual acuity at least by 18letters, at least by 21 letters, at least by 24 letters, at least by 27letters, at least by 30 letters, at least by 33 letters on the ETDRSchart or EVA test, depending on where the patient starts and efficacy ofthe particular course of treatment.

Based on in vitro results described above and in the examples withregard to the performance on a forced choice visual discrimination task,accuracy on a Bayesian stimulus reconstruction test, and performance onan error pattern test, and on the in vivo results described in theexamples, treatment with the inventive method will improve vision to34%, 41%, 45%, 49%, 53%, 58%, 64%, 70%, 76%, 80%, 84%, 87%, 91%, 96%,and 100% of normal visual acuity.

Objective electrophysiological tests in humans may consist of any of thefollowing:

One test is the flash visual evoked response (VEP), where an improvementconsists of a change from an absent response to a present response. Theappearance of a response is an objective indicator that visual signalsreach the brain (Chiappa 1997). This test provides a coarse measure ofvisual function; it indicates that signals have reached the brain. Itdoes not provide information about resolution.

Based on in vitro results described above and in the examples withregard to the performance on a forced choice visual discrimination task,accuracy on a Bayesian stimulus reconstruction test, and performance onan error pattern test, and on the in vivo results described in theexamples, treatment with the device will provide a positive result onthe flash visual evoked response.

A second test, one that addresses pattern signals, is the pattern VEP,either elicited by transient or steady-state stimuli, where animprovement consists of (a) a change from an absent response to apresent response or, (b) a decrease by a factor of two or more in thesmallest check size that leads to a detectable response, or, (c) anincrease by a factor of two or more in the spatial frequency that leadsto a detectable response. (a) is an objective indicator that visualsignals have reached the brain, as in the flash VEP test, above. (b) and(c) are objective indicators that visual resolution (acuity) hasimproved by a factor of two, and thus indicates an improvement that isrelevant to visual function and perception. Although the VEP is astandard clinical test, our use of it is different from the clinicalroutine, in which latency is the primary measurement (Chiappa 1997); ourgoal is to use it to measure acuity rather than detect conduction delay.By measuring the VEP as a function of check size or grating spatialfrequency, visual acuity can be determined (Bach, M et al 2008).

Based on in vitro results described above and in the examples withregard to the performance on a forced choice visual discrimination task,accuracy on a Bayesian stimulus reconstruction test, and performance onan error pattern test, and on the in vivo results described in theexamples, treatment with the device will lead to test results from thepattern VEP test as follows: (a) a change from an absent response to apresent response or, (b) a decrease by a factor of two or more in thesmallest check size that leads to a detectable response, and (c) anincrease by a factor of two or more in the spatial frequency that leadsto a detectable response.

Sweep VEP, where an improvement consists of (a) an increase by a factorof two or more in the spatial frequency that leads to a detectableresponse, or (b) a decrease by a factor of two or more in the minimumcontrast that leads to a detectable response. (a) is similar to acuitymeasured by the pattern VEP, above; (b) is an objective measure ofcontrast sensitivity (gray-level discrimination), which is also relevantto visual function. The sweep-VEP is established as a reliable objectivemeans to assess both acuity (Norcia and Tyler 1985) and contrastsensitivity (Norcia AM et al 1989).

Based on in vitro results described above and in the examples withregard to the performance on a forced choice visual discrimination task,accuracy on a Bayesian stimulus reconstruction test, and performance onan error pattern test, and on the in vivo results described in theexamples, treatment with the device will lead to test results from theSweep VEP test as follows: (a) an increase by a factor of two or more inthe spatial frequency that leads to a detectable response, and (b) adecrease by a factor of two or more in the minimum contrast that leadsto a detectable response.

For the above tests, the “factor of two” criterion for acuity is chosenbecause this is approximately a three-line improvement on a standardSnellen or ETDRS eyechart (e.g., from 20/400 to 20/200), a change thatis generally recognized as both statistically and functionallysignificant. Similarly, a “factor of two” criterion is chosen forcontrast sensitivity because this corresponds to a two-step improvementon the standard Pelli-Robson contrast-sensitivity eyechart (Pelli DG etal 1988), which is also generally recognized as both statistically andfunctionally significant.

Other methods to measure clinical efficacy are well known in the art.(Maguire et al 2008) Objective measures include, but not limited to,evaluation of the pupillary light reflex (PLR), full-fieldelectroretinography (ERG) (including bilateral full-field ERG), andnystagmus testing. International Society for Clinical Electrophysiologyof Vision standard guideline may be followed for the analyses. Pupilresponses may be recorded simultaneously in both eyes. (Kawasaki et al1995) Nystagmus may be characterized qualitatively and quantitatively byanalysis of motion paths in videos taken at baseline and at variousdesired time points post-treatment. Interpupillary distances may bemeasured directly from video frames. Subjective measures include, butnot limited to, standard tests of visual acuity (VA), kinetic visualfield, and mobility testing to assess the ability of the subjects tonavigate an obstacle course. For mobility testing, different mazes maybe used each time the test is performed and number of obstacles avoidedor hit, number of landmarks identified and time spent in the maze canthen be assessed. (Simonelli et al 2010)

The examples are offered to illustrate, but not to limit, the claimedinvention.

EXAMPLE 1 Method of Building the Encoders

Constructing the Encoders Using an Linear-Nonlinear-Poisson (LNP)Cascade

The parameters for the encoders were constructed from the responses totwo sets of stimuli: binary spatio-temporal white noise (WN) and agrayscale natural scene movie (NS) recorded in New York City's CentralPark. Both stimuli were presented at a frame rate of 15 Hz, and had thesame mean luminance (0.24 μW/cm² on the retina) and contrast(root-mean-squared (RMS) contrast was 0.087 μW/cm²). For thepreprocessing step, we chose a=0, and b=255/0.48 μW/cm², so that thevisual stimuli are mapped into the numerical range 0-255 (as describedabove in section entitled, “Encoders”.

To determine the spatiotemporal transformation, we used alinear-nonlinear model as described above in the same section (see also,Victor and Shapley 1979; Paninski et al. 2007; Pillow et al. 2008;Nirenberg et al. 2010). Parameters for the model were determined bymaximizing the likelihood that the model would produce theexperimentally-observed spike trains elicited by the stimuli, as inNirenberg et al, 2010; similar methods are in Paninski et al. 2007;Pillow et al. 2008, as maximum likelihood optimizations are well knownin the art.

For the data in the following examples, neurons were modeledindependently. For each neuron, m, the firing rate λ_(m) was determinedas in Eq. 1. Each neuron's linear filter was assumed to be a product ofa spatial function (on a 10×10 array of pixels, centered on thereceptive field) and a temporal function (18 time bins, 67 ms each,total duration 1.2 sec). Dimensionality was reduced by assuming thetemporal function to be a sum of 10 impulses and basis functions (raisedcosines in log time), as in Nirenberg et al., 2010, following Pillow etal. 2008.

The nonlinearities were parameterized as cubic spline functions with 7knots. Knots were spaced to cover the range of values given by thelinear filter output of the encoders.

As mentioned above, parameters were fit using a standard optimizationprocedure, as in Nirenberg et al, 2010, following Pillow et al, 2008,Paniniski, 2007. The quantity maximized is the log likelihood of theobserved spike trains under the model, as in Eq 2. Because each neuronis independent, the optimization of each neuron's parameters could becarried out independently. To maximize the log likelihood, we used thesame procedure as described in the text following Eq. 2 above, which webriefly reiterate here: We began by assuming that the nonlinearity N wasexponential, since in this case, the log likelihood Z has no localmaxima (Paninski, et al. 2007). After optimizing the linear filters andan exponential nonlinearity (by coordinate ascent), the nonlinearity wasreplaced by a spline. Final encoder parameters were then determined byalternating stages of maximizing the log likelihood with respect to (i)the spline parameters and (ii) the filter parameters, until a maximumwas reached, as described in (Nirenberg et al. 2010), which alsodiscusses the justification of this approach.

Models that take into account history dependence and correlations werealso built. Correlations between neurons were modeled using couplingkernels, following the method of (Pillow et al. 2008).

For the spike generation step, for each cell m, we created aninhomogeneous Poisson process with instantaneous firing rate λ_(m). Weconsider time intervals (bins) of length Δt=0.67 ms.

Note that FIGS. 3-6, 13 and 14 compare the performance of encoders andreal cells. FIGS. 7-9 also compare the performance of the encoders, whencombined with the transducers. For these experiments, the output of theencoders is passed through an interface that produces light pulses todrive the ChR2 in the ganglion cells. Two methods were used to take theoutput from the encoders and produce light pulses to drive ChR2. In thefirst method, the output of the encoders was used to control an LCDpanel (Panasonic PT-L104, Panasonic, Secaucus, N.J.). The LCD panel wasplaced in front of a set of 7 high-intensity blue LEDs (Cree XP-E Blue,Cree, Durham N.C.). Squares on the LCD panel conveyed the output of theencoders for the ganglion cell in the given location. For each frame,the squares were set to the highest intensity (255) if the encodersdictated that the ganglion cell should fire a spike within that frame,or the lowest intensity (0) if the ganglion cell should not fire a spikewithin that frame. If the LCD panel's intensity was high (255) at alocation, the light from the blue LEDs was passed through; if not, thelight was blocked. The output of the LCD panel was focused onto theretina. The intensity of the light at the 255 position at the retina was0.5 mW/mm². Each frame lasted 16.7 ms. A second method was used whereprecise spike timing was required. For this method, an LED (Cree XP-EBlue, Cree, Durham N.C.) drove the ganglion cells directly. The outputstate of the LED was controlled by a computer-generated 5V TTL pulse,which was sent through a control/amplification circuit as described byCampagnola et al., 2008. The LED turned on when the TTL pulse was high(5V), and off when the pulse was low (0V). The output of an encoder wasused to drive the TTL pulse through a computer's parallel port usingcustom software. When the encoder specified that a spike should occur,the TTL pulse was driven high (5V) for 1 ms, and then was turned offagain. The intensity of the LED pulse at the retina was 1 mW/mm² duringthe on state.

The responses of the transducer alone to visual stimuli (FIGS. 8C, 9D)were recorded using two methods. For the natural movie (FIG. 8C), theganglion cells were driven using the LED, again controlled by TTLpulses. The output of the LED was set to match the intensity of thenatural movie at a ganglion cell's receptive field location, using pulsecode modulation. TTL pulses were 1 ms wide. More pulses within a framerepresented brighter intensities, while fewer pulses represented dimmerintensities, with linear scaling between intensity and pulse rate. Thepulse rate of the LED was updated every 66.7 ms to match the intensityof the natural movie at that frame. The highest intensity of the moviewas mapped to the peak firing rate of the encoder for the given ganglioncell—this was typically between 8 and 12 pulses per 66.7 ms frame. Forthe baby face responses (FIG. 9D), the ganglion cells were driven usingthe LCD panel. The brightness of the LCD panel (0-255) was set to matchthe intensity of the baby face movie (0-255) at a given ganglion cell'sreceptive field location. The intensity of the LED was 1 mW/mm² at theretina, and the intensity of the LCD at maximum brightness was 0.5mW/mm², as described in the previous section.

EXAMPLE 2 Determining the Parameters for the SpatiotemporalTransformation

We describe a procedure to determine the parameters for thespatiotemporal transformations. Parameters discussed are as in thesection “Encoders” above.

In this example, first, the experiment is performed, and ganglion cellresponses to WN and NS stimuli are collected (see “Example 1—Method ofBuilding the Encoders” for an example of stimuli). Next, the reversecorrelation between the ganglion cell action potential times and thestimulus intensity is calculated, to determine a starting set of valuesfor the linear filter L_(m). Next, the linear filter is assumed to beseparable, a product of a spatial function and a temporal function. Thespatial function is parameterized as a 10 by 10 grid of weights, and thetemporal function is parameterized as the sum of 10 weighted temporalbasis functions. At this stage, the nonlinearity N_(m) is assumed to bean exponential function to ensure there are no local maxima. Next, thelikelihood for this set of parameters is calculated for the givenstimulus and recorded ganglion cell's responses. The next step is tofind the optimal parameters for the spatial function, temporal function,and exponential nonlinearity, by maximizing the likelihood of theseparameters using gradient ascent (as is well described, see: Paninski etal., 2007, Pillow et al., 2008, Nirenberg et al., 2010). After theseparameters are optimized, the exponential nonlinearity is replaced by a7-knot cubic spline, which more accurately describes the cell'sresponses. Next, the parameters of the spline are optimized to maximizethe likelihood. Subsequently, the parameters of the spatial and temporalfunctions are optimized to maximize the likelihood given the new splineparameters. These two steps (optimizing the spline parameters whileholding the spatial and temporal functions constant, then optimizing thespatial and temporal functions while holding the spline parametersconstant) are repeated until the change in likelihood from the two stepsis less than an arbitrarily chosen small number.

EXAMPLE 3 Comparison of Amount of Information Carried by Virtual RetinalCell and Real Retinal Cell

To build the data set, we recorded the responses of several hundredmouse retinal ganglion cells (515 cells) to a broad range of stimuli,including natural and artificial stimuli, which for this experiment wascheckerboard, natural scenes, and drifting gratings. For each cell, weconstructed its encoder (also referred to as its virtual retinal cell,or model cell). This was achieved as follows. We presented WN (whitenoise) and NS (natural or naturalistic stimuli) stimuli to retinas andrecorded the responses of the ganglion cells and parameterized thestimulus/response relationship for each cell, as described above. Wethen tested the encoders using additional natural scene and driftinggrating responses. Thus, all tests were performed using novel stimuli.

FIG. 3 shows the results of the information analysis. We recorded fromseveral hundred ganglion cells and modeled their responses. We thenpresented a large array of stimuli to both the model cells and the realcells—stimuli that were not used to build the encoders. We calculatedthe amount of information each virtual cell carried about the stimuliand compared it to the amount of information carried by its real cellcounterpart. As shown in the figure, the virtual cells carried nearlyall the information carried by the real cells. Each stimulus set waspresented to at least 100 real cells so that we had substantial data foreach analysis. We then assessed the robustness of the results bycarrying out the calculations multiple times. As expected, theinformation carried by the real cells increased with the increase intemporal resolution, and, as shown in the figure, the informationcarried by the virtual cells followed suit.

EXAMPLE 4 Comparison of Quality of Information Carried by VirtualRetinal Cell and Real Retinal Cell

FIG. 4 shows that the quality of the information carried by the virtualcells and the real cells is also the same. For each cell in FIG. 4, wecompared the posterior stimulus distributions generated by the virtualcell's responses with the posterior stimulus distributions generated bythe real cell's responses. FIG. 4A shows several examples, and FIG. 4Bshows histograms of the results for all the cells in the dataset.

To understand what the matrices show, we go through one in detail—theone in the top left corner of panel of panel A of FIG. 4-1. The verticalaxis gives the presented stimuli, and the horizontal axis gives the“decoded” stimuli (that is, the posterior distribution of stimuli). Inthe top row, there is a single bright square, and it is located at theleft-most position. What this means is that when the presented stimulusis the grating with the lowest temporal frequency, the decoded stimuluswill be correct—that is, the posterior stimulus distribution is sharplypeaked (as indicated by the single bright square), and the peak is atthe correct position (the position that corresponds to the lowesttemporal frequency). In contrast, in the bottom row of the matrix, thereis no single bright spot, just a stretch of red squares on the rightregion of the row. What this means is that when the presented stimulusis the highest temporal frequency grating, the decoding will likely fallshort—the posterior is broad and providing only limited informationabout what the stimulus is. It's indicating that the stimulus is likelya high frequency grating, but it's not indicating which high frequencyin particular.

The significance of this figure is two-fold. It shows, first, there aremany different kinds of posteriors among the real cells (e.g. there aremany types of ganglion cells in terms of their visual responses andsensitivities to stimuli); and, second, that the virtual cellsaccurately reproduce them, e.g., some cells provide information aboutlow frequencies, others provide information about high frequencies, orshow complex patterns, etc. But in nearly all cases, with severalhundred cells examined, the behavior of the real cell is captured by theencoder: The posterior produced by each virtual cell closely matchesthat produced by the real cell. This provides strong evidence that thevirtual cells can serve as proxies for the real cells.

EXAMPLE 5 Retinal Ganglion Cell Response Prediction by the Encoders

We used our encoders to make a set of predictions about the behavior ofthe ganglion cell classes, and then tested the predictions. Thepredictions in this case focused on differences in the way ON and OFFcells pull out motion information, specifically, slow motion.

This was achieved as follows. First, we constructed an encoder for thecell. We presented WN and NS stimuli to wt (wild type) retinas andrecorded the responses of the ganglion cells and parameterized thestimulus/response relationship as described above. The ganglion cellpopulation included both ON and OFF cells. We separately generatedparameters for ON and OFF cells and used the parameters to generate ONand OFF encoders. To make the predictions, we set up a visualdiscrimination task. We presented the different versions of the encoderwith drifting gratings that varied in temporal frequency and obtainedresponses. We then decoded the responses (using Bayesian (i.e. maximumlikelihood) as described herein). On each trial of the task, we asked:given the responses, what was the most likely frequency of the grating.Then, for all trials we tallied the fraction of times the correct answerwas obtained. To make specific predictions about ON and OFF cells, weperformed the task with populations made up exclusively of ON cells orexclusively of OFF cells. We also ran the task with encoders in whichthe parameters were determined using both scotopic (night light) andphotopic (daylight) light levels, since ganglion cells are known tobehave differently under these conditions (Purpura et al 1990; Troy etal 2005; Troy et al 1999).

Several results quickly emerged. The first one was that ON cells werebetter able to distinguish among low temporal frequencies (slow motion)than OFF cells, under scotopic conditions. The second was that OFF cellswere better able to distinguish among high temporal frequencies than ONcells, also under scotopic conditions. The third was that thesedifferences existed only under scotopic conditions: the two cell classesperformed approximately equally well under photopic conditions. Finally,the last one was that ON and OFF cells performed well only for a narrowrange of frequencies under scotopic conditions, but over a wide rangeunder photopic conditions.

We then tested the predictions. We started with electrophysiologicalmeasurements. We presented the same stimuli to the retina on amulti-electrode array and recorded ganglion cell responses. We thendecoded them as we decoded the virtual cell responses, i.e., usingmaximum likelihood. As shown in FIG. 5, the real cells make the samepredictions as the virtual cells, thus indicating, in a bottom linetest, that the virtual cells can serve as proxies for the real cells.

EXAMPLE 6 Animal Behavior Prediction by the Encoder

Finally, we moved to predictions about behavior. For this, we used anoptomotor task because it is a) simple, b) readily quantifiable, and c)allows us to selectively probe a single cell class by itself, the ONcells (only ON cells project to the accessory optic system (AOS), whichdrives this behavior) (Dann and Buhl 1987; Giolli et al 2005). In thistask, the animal (a wt mouse) is presented with a drifting grating, andit either tracks it or fails to track it. So to make predictions aboutbehavior, we asked the encoders the same question as we asked theanimal: is the grating present or absent? We used an approach parallelto the one used for testing predictions in the electrophysiologicalexperiments—that is, we decoded the responses using maximum likelihood.The only difference is that for the comparison with behavior, we decodedthe encoders' responses into just two alternatives (grating presentversus grating absent), since this corresponds to the alternatives ofthe behavioral task. Finally, for both the animal and the encoders, wepresented stimuli that represented photopic (daylight) or scotopic(night light) conditions and measured contrast sensitivity, which isdefined as the contrast at which 75 percent of the stimuli werecorrectly decoded, as is standard for 2-alternative forced choicepsychophysics. As shown in FIG. 6, the encoders correctly predict theshift in optomotor performance.

EXAMPLE 7 Retinal Ganglion Cell Firing Patterns Generated by theEncoders

We presented movies of natural scenes and recorded ganglion cellresponses from retinas taken from three groups of animals: a) normalanimals, (briefly: retinas were extracted from wild type (WT) mice; theretinas were then presented with movies of natural scenes, and thefiring patterns of the ganglion cells were recorded) (FIG. 7 top), b)blind animals that were treated with the retinal prosthetic (briefly:retinas were extracted from doubly transgenic mice bred in our lab fromcommercially available sources, which have retinal degeneration andwhich also express channelrhodopsin-2 in retinal ganglion cells; theretinas were presented with the encoded natural scene movies and thefiring patterns of the ganglion cells were recorded) (FIG. 7 middle),and c) blind animals treated with the approaches of current optogeneticprostheses (briefly: retinas were extracted from the same doublytransgenic mice as above; the retinas were then presented with naturalscene movies (no encoding) and ganglion cell firing patterns wererecorded) (FIG. 7 bottom).

In the normal retinas, the movies are converted into patterns of actionpotentials (also referred to as spike trains) by the retinal circuitry.The spike trains from the normal retinas are shown in FIG. 7, top. Inthe retinas from the blind animals treated with the encoder/transducermethod, the movies are converted into spike trains by theencoder/transducer (FIG. 7, middle). As shown in the figure, the spiketrains produced by this method closely match those produced by normalganglion cells. This happens because the encoders reproduce ganglioncell spike trains very reliably, and because ChR2 has fast enoughkinetics to follow the output of the encoders. Thus, we were able tomimic normal retinal input/output relations. For comparison, see FIG. 7,bottom; this shows the output of the standard optogenetic method (whichis just the transducer, i.e., just ChR2 as in Lagali et al 2008; Tomitaet al 2010; Bi A et al. 2006; Zhang et al. 2009; Thyagarajan et al.2010. In this case, the stimuli (the natural scene movies) areactivating the ChR2 directly. While this approach makes the ganglioncells fire, the firing patterns it produces are not the normal firingpatterns.

EXAMPLE 8 Performance of the Encoders and of the Retinal Prosthetic

We assessed the performance of the encoder and prosthetic in three ways:using a discrimination task method (FIG. 8), image reconstruction (FIG.9), and performance on a behavioral task (optomotor) (FIG. 10). Themeasures and results are presented below.

Performance on a Visual Discrimination Task

We started with the discrimination task. Briefly, we presented an arrayof stimuli and measured the extent to which they could be distinguishedfrom each other, based on the responses of the ganglion cells (orencoders). For ganglion cell recordings, stimuli were presented on acomputer monitor, and ganglion cell responses were recorded with amulti-electrode array as in Pandarinath et al, 2010.

To decode the responses in the test set, we determined which of thestimuli s_(j) was the most likely to produce it. That is, we determinedthe stimulus s_(j) for which p(r|s_(j)) was maximal. This was done viaBayes theorem, which states that p(s_(j)|r)=p(r|s_(j))p(s_(j))/p(r),where p(s_(j)|r) is the probability that the stimulus s_(j) was present,given a particular response r; p(r|s_(j)) is the probability ofobtaining a particular response r given the stimulus s_(j); and p(s_(j))is the probability that the stimulus s_(j) was present. Because p(s_(j))was set equal for all stimuli in this experiment, Bayes Theorem meansthat p(s|r_(j)) is maximized when p(r|s_(j)) is maximized. (Whenp(s_(j)) is uniform, as it was in this case, this method of finding themost likely stimulus given a response is referred to as maximumlikelihood decoding (Kass et al. 2005; Pandarinath et al. 2010; Jacobset al. 2009). For each presentation of stimulus s_(i) that resulted in aresponse r that was decoded as the stimulus s_(j), the entry at position(i,j) in the confusion matrix was incremented.

To build the response distributions needed for the decoding calculationsused to make the confusion matrices (i.e., to specify p(r|s_(j)) for anyresponse r), we proceeded as follows. The response r was taken to be thespike train spanning 1.33 sec after stimulus onset and binned with 66.7ms bins. Since the spike generation process is assumed to be aninhomogeneous Poisson process, the probability p(r|s_(j)) for the entire1.33 s response was calculated as the product of the probabilities foreach 66.7 ms bin. The probability assigned to each bin was determined byPoisson statistics, based on the average training set response in thisbin to the stimulus s_(j). Specifically, if the number of spikes of theresponse r in this bin is n, and the average number of spikes in thetraining set responses in this bin is h, then the probability assignedto this bin is (h^(n)/n!)exp(−h). The product of these probabilities,one for each bin, specifies the response distributions for the decodingcalculations used to make the confusion matrices. Results similar tothose shown in FIG. 8 were obtained with a range of bin sizes (50 to 100ms) and random assignments to training and test sets.

Once the confusion matrices were calculated, overall performance wasquantified by “fraction correct”, which is the fraction of times overthe whole task that the decoded responses correctly identified thestimuli. The fraction correct is the mean of the diagonal of theconfusion matrix. Given this procedure, we performed 4 sets of analyses.For each one, we used the responses from the WT retina for the trainingset and a different set of responses for the test set. We generated 4test sets.

(1) The first set consisted of responses from the WT retina. This isdone to obtain the fraction correct produced by normal ganglion cellresponses.

(2) The second set consisted of the responses from the encoders (theresponses from the encoders are, as indicated throughout this document,streams of electrical pulses, in this case, spanning 1.33 sec afterstimulus presentation, and binned with 66.7 ms, as are the WT ganglioncell responses). When we use the responses from the encoders as the testset, we obtain a measure of how well the encoders perform, given theresponse distributions of the normal WT retina. In other words, we startwith the assumption that the brain is built to interpret the responsesof the normal WT retina (i.e., the naturally encoded responses.) When weuse the responses from the encoders as our test set, we obtain a measureof how well the brain would do with our proxy of the normal retinalresponses (our proxy of the retina's code).

(3) The third set consisted of the responses from a blind animal drivenby the encoders and transducers (ChR2 in the ganglion cells), with theresponses of the same duration and bin size as above. This set gives usa measure of how well the encoders perform after their output has beenpassed through the transducer in real tissue. (While the transducerfollows the encoder very closely, it is not perfect, and this provides ameasure of how well the complete system (the encoders+transducers)performs.

(4) Finally, the last set consists of the responses from a blind animaldriven by just the transducers (ChR2 in the ganglion cells), withresponses of the same duration and bin size as above. This gives us ameasure of how well the standard optogenetic method performs.

The results are shown in FIG. 8. FIG. 8A shows the confusion matrixesgenerated when the test set was obtained from the normal WT retina. Onthe left are the matrices for individual ganglion cells, on the right,for a population of cells (20 cells). As shown, the individual cellseach carry a fair amount of information; together as a population, theycan discriminate nearly all stimuli in the set. The fraction correct was80%. FIG. 8B shows the confusion matrixes generated when the test setwas obtained from the encoders (note that these encoders were built fromthe input/output relations of the WT retina used in FIG. 8A). Thefraction correct was extremely close to that produced by the WT retina79%. FIG. 8C shows the results for the complete system (theencoders+transducers). The individual cells do not carry quite as muchinformation, but together as a population, they perform very well. Thefraction correct was 64%. Finally, FIG. 8D shows the results with thestandard optogenetic method. The individual cells here carry littleinformation, and even as a population, they are still quite limited. Thefraction correct was 7%, close to chance. Thus, the incorporation of theencoders, that is, the incorporation of our proxy of the retina's neuralcode, even for a small population of 20 cells, has a very large effectand can dramatically boosted prosthetic performance.

Finally, to summarize these data, we compared the percent performancesof the encoders alone (FIG. 8B), the encoders+transducers (FIG. 8C), andthe standard optogenetic method (FIG. 8D) to that of the normal retina(FIG. 8A). Results are as follows: the encoders' performance was 98.75%of the normal retina's performance, the complete system's performance,that is, the performance of the current embodiment of theencoders+transducers, was 80% of the normal retina's performance, andthe performance of the standard method (just transducer alone) was lessthan 10% of the normal retina's performance (8.75%).

Reconstructing Stimuli from the Ganglion Cell (or Encoder) Responses

Next, we performed stimulus reconstructions. Stimulus reconstructionuses a standard maximum likelihood approach to determine the most likelystimulus presented given a set of spike trains (reviewed in Paninski,Pillow, and Lewi, 2007). While the brain does not reconstruct stimuli,reconstructions serve as a convenient way to compare prosthetic methodsand to give an approximation of the level of visual restoration possiblewith each approach.

The stimulus consisted of a uniform gray screen for 1 second, followedby a given image for 1 second, preferably a human face. Note that eachpixel of the stimulus must span a reasonable region of visual space, sothat features of the image, in this case a face, can be discerned. Thiscriterion was satisfied by the choice of 35 by 35 pixels per face, asshown in FIG. 9. This is consistent with the fact that facialrecognition makes use of spatial frequencies at least as high as 8cycles per face, which requires at least 32 pixels in each dimension foradequate sampling (Rolls et al., 1985). In the example shown in FIG. 9,which uses mouse, each pixel corresponded to 2.6 degrees by 2.6 degreesof visual space. This in turn corresponds to approximately 12-20ganglion cells on the mouse retina.

Reconstructing the stimulus consists of a search over the space of allpossible stimuli to find the most likely stimulus given the measuredpopulation response r. To find the most likely stimulus given r, we usedBayes' theorem, p(s|r)=p(r|s)*p(s)/p(r). Because the a priori stimulusprobability p(s) is assumed to be constant for all s, maximizing p(s|r)is equivalent to maximizing p(r|s).

To determine p(r|s), it is assumed that the cells' responses areconditionally independent that is, it is assumed that p(r|s) is theproduct of the probabilities p(r_(j)|s), where p(r_(j)|s) is theprobability that the jth cell's response is r_(j), given the stimulus s.The rationale for this assumption is that it has been shown thatdeviations from conditional independence are small, and contribute onlya small amount to the information carried (Nirenberg et al, 2001; Jacobset al, 2009) and to the fidelity of stimulus decoding.

To calculate p(r_(m)|s) for a given cell m, the response r_(m) was takento be the spike train of the mth cell spanning 1 sec after stimulusonset and binned with 0.67 ms bins. Since the spike generation processis assumed to be an inhomogeneous Poisson process, the probabilityp(r_(m)|s) for the entire 1 sec response was calculated as the productof the probabilities assigned to each bin. The probability assigned toeach bin was determined by Poisson statistics based on the cell'sexpected firing rate in this bin to the stimulus s. The cell's expectedfiring rate is calculated from Eq. 1 (see section “The Encoders,” under“Spatiotemporal Transformation Step”), as the quantity λ_(m)(t;X), whereX in Eq. 1 is taken to be the stimulus s, and t is the time of the bin.Finally, the probability of the response for the population of cells,p(r|s), is calculated by multiplying the probabilities of the responsesof the individual cells p(r_(j)|s).

To find the most likely stimulus s_(j) for the population response, r,we used standard gradient ascent techniques. Since we wished to find thestimulus s_(j) that maximizes the probability distribution p(r|s), andthe stimulus space is high-dimensional, the gradient ascent methodprovides an efficient way to search through this high-dimensional space.Briefly, we began by starting at a random point in stimulus space,s_(k). We evaluated the probability distribution p(r|s_(k)) for thisstimulus, and also calculated the slope of this probability distributionwith respect to each dimension of the stimulus. We then created a newstimulus s_(k+1), by changing the stimulus s_(k) in the direction ofincreasing probability (as determined from the slope of the probabilitydistribution). This process continued iteratively until the probabilityof the stimulus increased only a marginal amount, i.e., until we reachedthe peak of p(r|s). Note that because the probability distribution isnot strictly log-concave, there exists the possibility of getting stuckin local maxima. To verify that this was not occurring, we performed thereconstructions using multiple random starting points and confirmed thatthey converged to the same peak.

To compare the performance of the prosthetic methods, we performedreconstructions using 3 sets of responses: 1) the responses of theencoders, 2) the responses from a blind retina, where the ganglion cellswere driven by the encoders+transducers (ChR2), and 3) responses from ablind animal, where the ganglion cells were driven by just thetransducers (i.e., just ChR2). The reconstructions were carried out onour processing cluster in blocks of 10×10 or 7×7 pixels.

The results are shown in FIG. 9. To obtain a large enough dataset forthe complete reconstruction, we moved the image systematically acrossthe region of retina we were recording from, so that responses to allparts of the image could be obtained with a single or small number ofretinas. Approximately 12,000 ganglion cell responses were recorded foreach image. FIG. 9A shows the original image. FIG. 9B shows the imageproduced by the responses of just the encoder. Not only is it possibleto tell that the image is a baby's face, but one can also tell that itis this particular baby's face, a particularly challenging task. FIG. 9Cshows the image produced by the responses from the encoders/transducers.While not quite as good, it's still close. Finally, FIG. 9D shows theimage produced by the responses from the standard method (i.e., justChR2). This image is much more limited. The results of this figure,again, indicate that incorporation of the retina's code has substantialimpact on the quality of the performance.

To quantify the differences in the performance of the methods, wecompared each method's reconstruction with the original image. To dothis, we calculated the standard Pearson correlation coefficient betweenthe reconstructed image's values at each pixel, and that of the realimage. Thus, a correlation coefficient of 1 indicates that all of theoriginal image's information was perfectly retained, while a correlationcoefficient of 0 indicates that the resemblance of the reconstruction tothe real image was no greater than chance.

Results were as follows: for the encoders alone, the correlationcoefficient was 0.897; for the encoders+transducers, the correlationcoefficient was 0.762, and for the transducers alone (corresponding tothe current art), the correlation coefficient was 0.159. Thus, just aswe found for the discrimination task, the performance of theencoders+transducers was several-fold better than the performance of thecurrent art.

Performance on an Optomotor Task.

Lastly, we performed a set of behavior experiments using an optomotortask. The results are shown in FIG. 10. Briefly, animals were presentedwith a drifting sine wave grating on a monitor and the animals' eyeposition was recorded with ISCAN PCI Pupil/Corneal Reflection TrackingSystems (ISCAN Corp., Woburn, Mass.). We later analyzed the recordingand correlated the motion with the motion of the stimulus. The leftpanel, FIG. 10A, shows the baseline drift (no stimulus). Blind animalsshow drift in eye position, similar to that observed with blind humans.FIG. 10B (the central column) shows the results for doubly transgenicmice bred in our lab from commercially available sources, which haveretinal degeneration and which also express channelrhodopsin-2 inretinal ganglion cells. These mice were shown the raw stimulus. Thismodels the standard optogenetic method. FIG. 10C (right column) showsthe results for a model our prosthetic. Doubly transgenic mice bred inour lab from commercially available sources, which have retinaldegeneration and which also express channelrhodopsin-2 in retinalganglion cells, were shown the output of our encoders instead of the rawstimulus. As shown in the figure, tracking was not produced by the micemodeling the standard optogenetic method, but was produced by the micemodeling our prosthetic. When the image has been converted into the codeused by the ganglion cells, the animal becomes able to track it.

EXAMPLE 9 Conversion from Images to Light Pulses

The schematic in FIG. 12 illustrates the conversion from image to lightpulses for an example encoder. FIG. 12A shows an example movie, a scenefrom Central Park. FIG. 12B shows the pre-processed movie. The meanintensity and contrast are scaled to match the operating range of thespatiotemporal transformation. In this example movie, no mean orcontrast rescaling was required. FIG. 12B also indicates the position ofthe example encoder that produces the output in FIGS. 12C-E. FIG. 12Cshows the output of the spatiotemporal transformation step. Thepre-processed movie is convolved with the example cell's spatiotemporalkernel and passed through its nonlinearity to produce a firing rate.FIG. 12D shows the output of the spike generation step. The firing rateproduced by the spatiotemporal transformation is passed through thespike generator, which produces a series of electronic pulses. FIG. 12Eshows the light pulses that correspond to the output produced by thespike generation step.

EXAMPLE 10 Examples of Parameter Sets for Mouse and Monkey RetinalGanglion Cell Encoders

In this example we provide sets of parameters for two sample encoders: amouse encoder and a monkey encoder. The parameter sets consist ofspatial parameters, temporal parameters, and nonlinearity (spline)parameters. In addition, we provide the basis functions that are used toconstruct the temporal function (detailed in the section “Encoders”under the heading “Spatiotemporal Transformation Step”).

Example Set of Encoder Parameters for a Mouse Ganglion Cell

Spatial parameters—each number is a weight at a location in space on the10×10 grid. Each location on the grid is spaced by 2.6 degrees of visualangle. The sample weights below have been scaled by 10³ for readability.

${Row}_{1} = \begin{bmatrix}\begin{matrix}0.33002 & 0.04921 & 0.35215 & {- 0.50472} & {- 0.31662}\end{matrix} \\\begin{matrix}0.48097 & 1.59118 & 0.25387 & {- 0.29734} & {- 0.65491}\end{matrix}\end{bmatrix}$ ${Row}_{2} = \begin{bmatrix}\begin{matrix}0.72320 & {- 0.79947} & 1.11129 & {- 0.42650} & {- 0.10557}\end{matrix} \\\begin{matrix}{- 0.83933} & 1.09369 & {- 0.06499} & {- 0.22048} & 0.93292\end{matrix}\end{bmatrix}$ ${Row}_{3} = \begin{bmatrix}\begin{matrix}0.06408 & 0.11642 & 0.04056 & {- 1.00307} & 0.76165\end{matrix} \\\begin{matrix}0.40809 & {- 0.92745} & 0.80737 & 0.92201 & {- 0.12520}\end{matrix}\end{bmatrix}$ ${Row}_{4} = \begin{bmatrix}\begin{matrix}0.48629 & 0.70789 & 0.15863 & 0.28964 & {- 0.12602}\end{matrix} \\\begin{matrix}{- 0.31769} & 0.29873 & {- 0.05653} & {- 0.13206} & 0.65947\end{matrix}\end{bmatrix}$ ${Row}_{5} = \begin{bmatrix}\begin{matrix}1.38570 & {- 0.92340} & {- 0.37912} & 1.43493 & {- 0.56229}\end{matrix} \\\begin{matrix}0.33423 & 0.17084 & {- 0.21360} & 1.19797 & 2.19499\end{matrix}\end{bmatrix}$ ${Row}_{6} = \begin{bmatrix}\begin{matrix}0.06191 & {- 0.92478} & 0.56671 & 0.30621 & {- 0.52551}\end{matrix} \\\begin{matrix}0.75282 & {- 1.19834} & 0.99852 & 1.59545 & 2.82842\end{matrix}\end{bmatrix}$ ${Row}_{7} = \begin{bmatrix}\begin{matrix}{- 0.20276} & {- 1.03567} & 0.74796 & {- 0.59916} & 0.48170\end{matrix} \\\begin{matrix}0.31746 & 1.22590 & 1.52443 & 2.79257 & 1.82781\end{matrix}\end{bmatrix}$ ${Row}_{8} = \begin{bmatrix}\begin{matrix}0.31473 & 0.46495 & 0.51243 & 0.19654 & 0.91553\end{matrix} \\\begin{matrix}0.05541 & {- 0.80165} & 2.12634 & 1.46123 & 1.49243\end{matrix}\end{bmatrix}$ ${Row}_{9} = \begin{bmatrix}\begin{matrix}{- 0.12374} & {- 1.08114} & 0.69296 & 0.03668 & {- 0.16194}\end{matrix} \\\begin{matrix}{- 0.02616} & 0.22097 & 0.79908 & {- 0.05111} & 0.54044\end{matrix}\end{bmatrix}$ ${Row}_{10} = \begin{bmatrix}\begin{matrix}0.06479 & {- 0.00645} & {- 0.83147} & 0.10406 & 0.60743\end{matrix} \\\begin{matrix}{- 0.87956} & 1.53526 & 0.02914 & 0.23768 & {- 0.13274}\end{matrix}\end{bmatrix}$

Temporal parameters—There are 10 temporal parameters. Each number is aweight for the 10 temporal basis functions (given next).

$\quad\begin{bmatrix}\begin{matrix}11.84496 & {- 5.03720} & {- 42.79105} & {- 173.22514} & {- 172.80439}\end{matrix} \\\begin{matrix}4.02598 & 186.79332 & 6.04702 & 50.69707 & {- 67.50911}\end{matrix}\end{bmatrix}$

Temporal basis functions—There are 10 temporal basis functions {F₁, F₂,. . . F₁₀}. Each function has 18 values, where each value defines thebasis function for a given timestep. The timesteps are spaced by 66.7ms. The first value represents the function at a lag of 66.7 ms, and thelast value represents the function at a lag of 1.2 s.

$F_{1} = \begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{bmatrix}$ $F_{2} = \begin{bmatrix}0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{bmatrix}$ $F_{3} = \begin{bmatrix}0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{bmatrix}$ $F_{4} = \begin{bmatrix}0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{bmatrix}$ $F_{5} = \begin{bmatrix}0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{bmatrix}$ $F_{6} = \begin{bmatrix}\begin{matrix}0 & 0 & 0 & 0 & 0 & 0.8958 & 0.4425 & 0.0418\end{matrix} \\\begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{matrix}\end{bmatrix}$ $F_{7} = \begin{bmatrix}\begin{matrix}0 & 0 & 0 & 0 & 0 & 0.3685 & 0.7370 & 0.5240\end{matrix} \\\begin{matrix}0.2130 & 0.0325 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{matrix}\end{bmatrix}$ $F_{8} = \begin{bmatrix}\begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & 0.3038 & 0.5724 & 0.5724\end{matrix} \\\begin{matrix}0.4236 & 0.2469 & 0.1069 & 0.0250 & 0 & 0 & 0 & 0 & 0\end{matrix}\end{bmatrix}$ $F_{9} = \begin{bmatrix}\begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & 0.0000 & 0.1420 & 0.3493\end{matrix} \\\begin{matrix}0.4696 & 0.4874 & \begin{matrix}0.4336 & 0.3439 & 0.2457\end{matrix}\end{matrix} \\\begin{matrix}0.1563 & 0.0852 & 0.0358 & 0.0081\end{matrix}\end{bmatrix}$ $F_{10} = \begin{bmatrix}\begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.0195\end{matrix} \\\begin{matrix}0.1233 & 0.2465 & \begin{matrix}0.3441 & 0.4012 & 0.4187\end{matrix}\end{matrix} \\\begin{matrix}0.4043 & 0.3678 & 0.3181 & 0.2626\end{matrix}\end{bmatrix}$

Note that the above numbers are not model parameters, i.e. they are notfitted to the data, but are chosen a priori. F₁ through F₅ are impulses,and F₆ through F₁₀ are raised cosines in logarithmic time, whose valuesare given here for the reader's convenience.

Spline parameters—the nonlinearity is a standard cubic spline, i.e. apiecewise cubic polynomial. As is standard, the spline is defined interms of its constituent polynomials {P₁, P₂, . . . P₆} and knots {b₁,b₂, . . . b₇}. Each P_(n) is used to compute the nonlinearity betweenthe pair of knots b_(n) and b_(n+1). Since here, the number ofpolynomials p_(tot)=6, there are p_(tot)+1=7 knots. Each polynomial P,is defined by 4 coefficients [A_(n), B_(n), C_(n), D_(n)]. For a givenpoint x, where b_(n)≦x≦b_(n+1), the value of the nonlinearity y is foundby:y=((A _(n)(x−b _(n))+B _(n))(x−b _(n))+C _(n))(x−b _(n))+D _(n)For values of x that are less than b₁, the above formula is used withn=1. For values of x that are greater than b₇, the above formula is usedwith n=7.

${Knots}{\text{:}\mspace{14mu}\begin{bmatrix}\begin{matrix}{- 4.2105} & {- 2.6916} & {- 1.1727}\end{matrix} \\\begin{matrix}0.3461 & 1.8650 & 3.3839 & 4.9027\end{matrix}\end{bmatrix}}$ $P_{1} = \begin{bmatrix}0.2853 & {- 0.1110} & {- 2.9797} & 4.8119\end{bmatrix}$ $P_{2} = \begin{bmatrix}{- 0.2420} & 1.1890 & {- 1.3423} & 1.0298\end{bmatrix}$ $P_{3} = \begin{bmatrix}{- 0.2063} & 0.0863 & 0.5947 & 0.8860\end{bmatrix}$ $P_{4} = \begin{bmatrix}3.3258 & {- 0.8538} & {- 0.5712} & 1.2653\end{bmatrix}$ $P_{5} = \begin{bmatrix}{- 6.3887} & 14.3006 & 19.8527 & 10.0815\end{bmatrix}$ $P_{6} = \begin{bmatrix}3.2260 & {- 14.8100} & 19.0790 & 50.8402\end{bmatrix}$Example Set of Encoder Parameters for a Monkey Ganglion Cell

Spatial parameters—each number is a weight at a location in space on the10×10 grid. Each location on the grid is spaced by 0.3 degrees of visualangle. The sample weights below have been scaled by 10³ for readability.

$\mspace{20mu}{{Row}_{1} = \begin{bmatrix}\begin{matrix}0.55195 & {- 0.84156} & 0.84613 & {- 0.57117} & {- 0.19474}\end{matrix} \\\begin{matrix}{- 0.11197} & {- 1.00783} & {- 0.03454} & 1.28868 & {- 0.22166}\end{matrix}\end{bmatrix}}$ $\mspace{20mu}{{Row}_{2} = \begin{bmatrix}\begin{matrix}{- 1.04227} & 0.23179 & 0.25551 & {- 0.45285} & {- 0.41161}\end{matrix} \\\begin{matrix}{- 0.15036} & 0.83755 & {- 1.57133} & {- 0.88564} & 2.05603\end{matrix}\end{bmatrix}}$ $\mspace{20mu}{{Row}_{3} = \begin{bmatrix}\begin{matrix}0.60746 & 0.53720 & 0.60018 & {- 2.29069} & {- 1.81365}\end{matrix} \\\begin{matrix}{- 0.50460} & {- 1.29800} & {- 1.45387} & 1.58825 & {- 1.17287}\end{matrix}\end{bmatrix}}$ ${Row}_{4} = \begin{bmatrix}\begin{matrix}{- 0.22411} & {- 0.77299} & {- 1.00706} & {- 1.94835} & {- 2.92171}\end{matrix} \\\begin{matrix}{- 2.98774} & {- 1.23428} & {- 0.54277} & 0.68372 & {- 0.70579}\end{matrix}\end{bmatrix}$ $\mspace{20mu}{{Row}_{5} = \begin{bmatrix}\begin{matrix}0.06135 & 0.22591 & {- 3.75132} & {- 3.01549} & {- 2.58498}\end{matrix} \\\begin{matrix}{- 2.18981} & 0.13431 & {- 0.82007} & {- 1.10427} & {- 0.10170}\end{matrix}\end{bmatrix}}$ $\mspace{20mu}{{Row}_{6} = \begin{bmatrix}\begin{matrix}0.99720 & {- 0.02322} & 0.43823 & {- 0.52735} & {- 2.14156}\end{matrix} \\\begin{matrix}{- 2.89650} & {- 0.57703} & {- 0.87173} & 0.83669 & 1.35836\end{matrix}\end{bmatrix}}$ $\mspace{20mu}{{Row}_{7} = \begin{bmatrix}\begin{matrix}0.13385 & 0.76995 & {- 0.80099} & {- 0.11574} & {- 1.70100}\end{matrix} \\\begin{matrix}{- 0.51437} & 0.29501 & {- 2.02754} & {- 0.22178} & {- 1.26073}\end{matrix}\end{bmatrix}}$ $\mspace{20mu}{{Row}_{8} = \begin{bmatrix}\begin{matrix}{- 0.69551} & 1.30671 & {- 0.91948} & 0.15329 & 0.30121\end{matrix} \\\begin{matrix}0.20764 & {- 1.69209} & {- 0.09721} & {- 0.09431} & 0.36469\end{matrix}\end{bmatrix}}$ $\mspace{20mu}{{Row}_{9} = \begin{bmatrix}\begin{matrix}0.26733 & {- 0.01433} & 0.57732 & 0.13921 & {- 0.18279}\end{matrix} \\\begin{matrix}0.36743 & {- 0.59386} & 0.71287 & {- 1.03279} & 0.09482\end{matrix}\end{bmatrix}}$ $\mspace{20mu}{{Row}_{10} = \begin{bmatrix}\begin{matrix}1.17775 & {- 0.90456} & {- 1.58663} & {- 1.14128} & 0.00673\end{matrix} \\\begin{matrix}0.20418 & 0.98834 & {- 0.78054} & 0.43434 & 0.52536\end{matrix}\end{bmatrix}}$

Temporal parameters—There are 10 temporal parameters. Each number is aweight for the 10 temporal basis functions (given next).

$\quad\begin{bmatrix}\begin{matrix}25.67952 & {- 43.25612} & 15.94787 & {- 84.80078} & {- 88.11922}\end{matrix} \\\begin{matrix}{- 4.70471} & {- 45.63036} & 73.07752 & 34.14097 & {- 0.95146}\end{matrix}\end{bmatrix}$

Temporal basis functions—There are 10 temporal basis functions {F₁, F₂,. . . F₁₀}. Each function has 30 values, where each value defines thebasis function for a given timestep. The timesteps are spaced by 16.7ms. The first value represents the function at a lag of 16.7 ms, and thelast value represents the function at a lag of 0.5 s.

$\mspace{20mu}{F_{1} = \begin{bmatrix}\begin{matrix}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{matrix} \\\begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{matrix}\end{bmatrix}}$ $\mspace{20mu}{F_{2} = \begin{bmatrix}\begin{matrix}0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{matrix} \\\begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{matrix}\end{bmatrix}}$ $\mspace{20mu}{F_{3} = \begin{bmatrix}\begin{matrix}0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{matrix} \\\begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{matrix}\end{bmatrix}}$ $\mspace{20mu}{F_{4} = \begin{bmatrix}\begin{matrix}0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{matrix} \\\begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{matrix}\end{bmatrix}}$ $\mspace{20mu}{F_{5} = \begin{bmatrix}\begin{matrix}0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{matrix} \\\begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{matrix}\end{bmatrix}}$ $\mspace{20mu}{F_{6} = \begin{bmatrix}\begin{matrix}\begin{matrix}0 & 0 & 0 & 0 & 0 & 0.8625 & 0.4952 & 0.1045 & 0 & 0 & 0 & 0 & 0\end{matrix} \\\begin{matrix}0 & 0 & 0 & \begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{matrix}\end{matrix}\end{matrix} \\\begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{matrix}\end{bmatrix}}$ $\mspace{20mu}{F_{7} = \begin{bmatrix}\begin{matrix}\begin{matrix}0 & 0 & 0 & 0 & 0 & 0.3396 & 0.6754 & 0.5612 & 0.3153\end{matrix} \\\begin{matrix}0.1180 & 0.0172 & \begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{matrix}\end{matrix}\end{matrix} \\\begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{matrix}\end{bmatrix}}$ $\mspace{20mu}{F_{8} = \begin{bmatrix}\begin{matrix}\begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & 0.2309 & 0.4765 & 0.5415 & 0.4765\end{matrix} \\\begin{matrix}0.3562 & 0.2309 & \begin{matrix}0.1266 & 0.0535 & 0.0125 & 0 & 0\end{matrix}\end{matrix}\end{matrix} \\\begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{matrix}\end{bmatrix}}$ $F_{9} = \begin{bmatrix}\begin{matrix}\begin{matrix}\begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.0753 & 0.2323 & 0.3583\end{matrix} \\\begin{matrix}0.4226 & 0.4312 & 0.4002 & \begin{matrix}0.3461 & 0.3461 & 0.2819 & 0.2819\end{matrix}\end{matrix}\end{matrix} \\\begin{matrix}0.2168 & 0.1567 & 0.1052 & 0.0639 & 0.0333\end{matrix}\end{matrix} \\\begin{matrix}0.0131 & 0.0024 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{matrix}\end{bmatrix}$ $\mspace{20mu}{F_{10} = \begin{bmatrix}\begin{matrix}\begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.0004 & 0.0420 & 0.1189\end{matrix} \\\begin{matrix}0.1990 & 0.2656 & \begin{matrix}0.3124 & 0.3386 & 0.3466 & 0.3398\end{matrix}\end{matrix}\end{matrix} \\\begin{matrix}\begin{matrix}0.3219 & 0.2962 & 0.2656 & 0.2326\end{matrix} \\\begin{matrix}0.1990 & 0.1662 & 0.1354 & 0.1071\end{matrix} \\\begin{matrix}0.0820 & 0.0603 & 0.0420 & 0.0272 & 0.0158\end{matrix}\end{matrix}\end{bmatrix}}$

Spline parameters—the nonlinearity is a standard cubic spline, i.e. apiecewise cubic polynomial. As is standard, the spline is defined interms of its constituent polynomials {P₁, P₂, . . . P₆} and knots {b₁,b₂, . . . b₇}. Each P, is used to compute the nonlinearity between thepair of knots b_(n) and b_(n+1). Since here, the number of polynomialsp_(tot)=6, there are p_(tot)+1=7 knots. Each polynomial P_(n) is definedby 4 coefficients [A_(n), B_(n), C_(n), D_(n)]. For a given point x,where b_(n)≦x≦b_(n+1), the value of the nonlinearity is found by:

y = ((A_(n)(x − b_(n)) + B_(n))(x − b_(n)) + C_(n))(x − b_(n)) + D_(n)${Knots}{\text{:}\mspace{14mu}\begin{bmatrix}\begin{matrix}{- 7.9291} & {- 5.9389} & {- 3.9486}\end{matrix} \\\begin{matrix}{- 1.9584} & 0.0318 & 2.0221 & 4.0123\end{matrix}\end{bmatrix}}$ $P_{1} = \begin{bmatrix}{- 1.0067} & 3.4136 & 4.5376 & {- 25.8942}\end{bmatrix}$ $P_{2} = \begin{bmatrix}{- 0.2910} & {- 2.5970} & 6.1628 & {- 11.2780}\end{bmatrix}$ $P_{3} = \begin{bmatrix}2.4072 & {- 4.3345} & {- 7.6326} & {- 11.5935}\end{bmatrix}$ $P_{4} = \begin{bmatrix}{- 2.7537} & 10.0384 & 3.7195 & {- 24.9763}\end{bmatrix}$ $P_{5} = \begin{bmatrix}1.6687 & {- 6.4032} & 10.9543 & 0.4804\end{bmatrix}$ $P_{6} = \begin{bmatrix}{- 1.0485} & 3.5605 & 5.2966 & 10.0743\end{bmatrix}$

EXAMPLE 11 Monkey Retinal Ganglion Cell Firing Patterns Generated By theEncoders

We presented movies of natural scenes and recorded ganglion cellresponses of retinas taken from macaque monkeys (briefly: retinas wereextracted from monkeys; the retinas were presented with movies ofnatural scenes, and ganglion cell responses were recorded) (FIG. 13top). In addition, we presented the movies to encoders generated forthese monkey ganglion cells (following the procedures outlined in thesection “Encoders”). (FIG. 13 middle).

In the normal retinas, the movies are converted into patterns of actionpotentials, also referred to as spike trains, by the retinal circuitry.The spike trains from the normal retinas are shown in FIG. 13, top. Theresponses produced by the encoders closely match these responses (FIG.13, middle). Thus, we were able to mimic normal retinal input/outputrelations.

EXAMPLE 12 Performance of the Monkey Encoders on a Visual DiscriminationTask

We assessed the performance of a set of monkey encoders using adiscrimination task method (FIG. 14). This task followed the methodoutlined in Example 8 (see section “Performance in a discriminationtask”).

Using the procedure outlined in Example 8, we performed 2 sets ofanalyses. For each one, we used the responses from the monkey retina forthe training set. For the test sets, we used two sets of responses:

(1) The first set consisted of responses from the monkey retina. This isdone to obtain the fraction correct produced by normal ganglion cellresponses.

(2) The second set consisted of the responses from the encoders (theresponses from the encoders are, as indicated throughout this document,streams of electrical pulses, in this case, spanning 1.33 sec afterstimulus presentation, and binned with 66.7 ms, as are the monkeyganglion cell responses).

When we use the responses from the encoders as the test set, we obtain ameasure of how well the encoders perform, given the responsedistributions of the monkey retina. In other words, we start with theassumption that the brain is built to interpret the responses of themonkey retina (i.e., the naturally encoded responses.) When we use theresponses from the encoders as our test set, we obtain a measure of howwell the brain would do with our proxy of the normal retinal responses(our proxy of the retina's code). The results are shown in FIG. 14. FIG.14A shows the confusion matrixes generated when the test set wasobtained from the monkey retina. On the left are the matrices forindividual ganglion cells, on the right, for a population of cells (10cells). As shown, the individual cells each carry a fair amount ofinformation; together as a population, they can discriminate nearly allstimuli in the set. The fraction correct was 83%. FIG. 14B shows theconfusion matrixes generated when the test set was obtained from theencoders (encoders built from the input/output relations of the monkeyretina e.g., as shown in FIG. 14A). The fraction correct produced by theresponses of the encoders, 77%, was extremely close to the fractioncorrect produced by the responses of the normal monkey ganglion cells,83%. That is, it was 77/83=92.7% that of the fraction correct producedby the normal monkey ganglion cells. Thus, the encoders' output, thatis, our proxy of the monkey retina's neural code, nearly matches theperformance of the monkey retina.

EXAMPLE 13 Fidelity of Transducers' Output to Encoders' Output

FIG. 15 shows that ganglion cell responses produced by theencoders+transducers follow the encoded output with high fidelity. Anencoder was created as described above. A stimulus, an image of a baby'sface, is input into a processing device running the encoder, and a codeis generated. The code is put through an interface to drive an LED thatis positioned above the retina, taken from a doubly transgenic mousethat is blind and that expresses ChR2. Electrodes record the retinalresponse. FIG. 15A shows the light pulses and the corresponding ganglioncell output. For each pair of rows, the top row shows the times of thelight pulses, while the bottom row shows the times of the actionpotentials produced by the ChR2-expressing ganglion cell. FIG. 15B thenshows an expansion of the circled regions from FIG. 15A, demonstratingone-to-one correspondence between light pulses and action potentials. Asthe figure shows, the action potentials can follow the light pulses, andtherefore, the encoder, with high fidelity.

EXAMPLE 14 Treatment with Prosthetic

A male 53-year-old patient presents with macular degeneration. He isgiven the EVA test and scores a 48—his vision is 20/200 and he isdiagnosed with low vision. His vision has been steadily worsening and heis concerned about becoming completely blind. The physician discussestreatment using the retinal prosthetic with the patient and it isdecided to treat the patient with the retinal prosthetic of theinvention.

A kit with the gene therapy drug as described above and the devicehaving a camera, processor, and interface are used.

To reduce the risk of an ocular immune response to the treatment, thepatient is administered a short course of glucocorticoids and an officevisit is scheduled for the end of the course. During the office visit,gene therapy with a rAAV vector carrying a channelrhodopsin-2 cDNA, withpromoter sequences targeting retinal ganglion cells is administered tothe patient via intravitreal injection under local anesthetic.

The patient recovers and is sent home. There are weekly follow-up visitsto ensure the eye heals properly and to monitor for dissemination of theviral vector. The eye heals normally and no dissemination is found.

On the fourth week, the patient is fitted for the first time with thehardware component of the treatment, which comprises a pair of glassesthat include a processor and battery. Each lens of the glasses is acamera that records images; the inward-facing surface of each lens is alight array.

An initial visual acuity test is taken with and without the glassesdevice. The patient's vision without the glasses remains 20/200 with thetherapeutic device it has already improved to 20/80 as measured withEVA. Each week the patient returns and is tested again and spends timepracticing use of the complete device; by the sixth week vision with theglasses visual acuity has increased to 20/50. The patient hasnear-normal vision.

EXAMPLE 15 Treatment with the Prosthetic

A female, 60 year old patient presents with macular degeneration. She isgiven the EVA test and scores 3 letters—her vision is 20/800 and she isdetermined to be legally blind. The physician discusses treatment usingthe retinal prosthetic with the patient and it is decided to treat thepatient with the retinal prosthetic of the invention.

A kit with the gene therapy drug and the device having a camera,processor, and interface are used.

To reduce the risk of an ocular immune response to the treatment, thepatient is administered a short course of glucocorticoids and an officevisit is scheduled for the end of the course. During the visit, genetherapy is administered to the patient via intravitreal injection underlocal anesthetic.

The patient recovers and is sent home. There are weekly follow-up visitsto ensure the eye heals properly and to monitor for dissemination of theviral vectors. The eye heals normally and no dissemination is found.

On the fourth week, the patient is fitted for the first time with thehardware component of the treatment, which comprises a pair of glassesthat include a processor and battery. Each lens of the glasses is acamera that records images; the inward-facing surface of each lens is alight array.

An initial visual acuity test is taken with and without the glassesdevice. The patient's vision without the glasses remains 20/800; withthe therapeutic device it has already improved to 20/100 as measured bystandard visual acuity tests. Each week the patient returns and istested again and spends time practicing use of the complete device; bythe sixth week vision with the glasses visual acuity has increased to20/40.

EXAMPLE 15 Encoder Performance

FIGS. 16A-F illustrates the performance of retinal encoder models forvarious cells (cells 1-6, respectively) when tested with movies ofnatural scenes, including landscapes, people walking, etc. In eachfigure, the performance of a conventional linear-nonlinear (LN) model isshown on the left, and the performance of the linear-nonlinear (LN)model of the type described in this application is shown on the right.Performance is shown via raster plots and peri-stimulus time histograms(PSTHs). The conventional (LN) model was developed based only on theexperimental response of retinal cells to a white noise stimulus. Incontrast, the linear-nonlinear (LN) models of the type described in thisapplication are developed based on recorded cell responses to both whitenoise and natural scene stimuli.

For the examples shown, the input test stimulus for both types of modelsis a movie of natural scenes, taken in Central Park in New York City. Asshown, the standard LN model is not highly effective on natural scenestimuli: that is, this model, which is built using white noise stimuli,does not produce spike patterns that closely match those of the realcell. In contrast, the LN model described in this application, which isbuilt using white noise and natural scene stimuli, is highly effective.The spike patterns it produces closely match those of the real cell.(Note that the natural scene movie used to test the models is differentfrom that used to train the models, as is required for validating anymodel. Note also that in each figure, the same real cell is used as thebasis for both types of models. Finally, note that performance of theencoder models of the type described herein has been demonstrated with ahost of other stimuli, including movies, of faces, people walking,children playing, landscapes, trees, small animals, etc., as shown inthe Prosthetic Application, and in Nirenberg, et al. Retinal prostheticstrategy with the capacity to restore normal vision, PNAS 2012 and theaccompanying Supplementary Information section available atwww.pnas.org/lookup/suppl/doi:10.1073/pnas.1207035109/-/DCSupplemental).

The same conclusions about performance can be drawn from the PSTHs. Thelight gray trace shows the average firing rate of the real cell; thedark grey trace shows the average firing rate of the model cell. Thestandard LN model misses many features of the firing rate; each of thedifferent FIGS. 16A-16F, show examples of the different features missedby the standard model. The model described in this application, though,captures the features of the firing rates reliably and does so for anarray of different cells (many other examples are shown in the herein).

The scope of the present invention is not limited by what has beenspecifically shown and described hereinabove. Those skilled in the artwill recognize that there are suitable alternatives to the depictedexamples of materials, configurations, constructions and dimensions.Numerous references, including patents and various publications, arecited and discussed in the description of this invention and attachedreference list. The citation and discussion of such references isprovided merely to clarify the description of the present invention andis not an admission that any reference is prior art to the inventiondescribed herein. All references cited and discussed in thisspecification are incorporated herein by reference in their entirety.

While various inventive embodiments have been described and illustratedherein, those of ordinary skill in the art will readily envision avariety of other means and/or structures for performing the functionand/or obtaining the results and/or one or more of the advantagesdescribed herein, and each of such variations and/or modifications isdeemed to be within the scope of the inventive embodiments describedherein. More generally, those skilled in the art will readily appreciatethat all parameters, dimensions, materials, and configurations describedherein are meant to be exemplary and that the actual parameters,dimensions, materials, and/or configurations will depend upon thespecific application or applications for which the inventive teachingsis/are used. Those skilled in the art will recognize, or be able toascertain using no more than routine experimentation, many equivalentsto the specific inventive embodiments described herein. It is,therefore, to be understood that the foregoing embodiments are presentedby way of example only and that, within the scope of the appended claimsand equivalents thereto, inventive embodiments may be practicedotherwise than as specifically described and claimed. Inventiveembodiments of the present disclosure are directed to each individualfeature, system, article, material, kit, and/or method described herein.In addition, any combination of two or more such features, systems,articles, materials, kits, and/or methods, if such features, systems,articles, materials, kits, and/or methods are not mutually inconsistent,is included within the inventive scope of the present disclosure.

The above-described embodiments can be implemented in any of numerousways. For example, the embodiments may be implemented using hardware,software or a combination thereof. When implemented in software, thesoftware code can be executed on any suitable processor or collection ofprocessors, whether provided in a single computer or distributed amongmultiple computers.

Further, it should be appreciated that a computer may be embodied in anyof a number of forms, such as a rack-mounted computer, a desktopcomputer, a laptop computer, or a tablet computer. Additionally, acomputer may be embedded in a device not generally regarded as acomputer but with suitable processing capabilities, including a PersonalDigital Assistant (PDA), a smart phone or any other suitable portable orfixed electronic device.

Also, a computer may have one or more input and output devices. Thesedevices can be used, among other things, to present a user interface.Examples of output devices that can be used to provide a user interfaceinclude printers or display screens for visual presentation of outputand speakers or other sound generating devices for audible presentationof output. Examples of input devices that can be used for a userinterface include keyboards, and pointing devices, such as mice, touchpads, and digitizing tablets. As another example, a computer may receiveinput information through speech recognition or in other audible format.

Such computers may be interconnected by one or more networks in anysuitable form, including a local area network or a wide area network,such as an enterprise network, and intelligent network (IN) or theInternet. Such networks may be based on any suitable technology and mayoperate according to any suitable protocol and may include wirelessnetworks, wired networks or fiber optic networks.

A computer employed to implement at least a portion of the functionalitydescribed herein may include a memory, one or more processing units(also referred to herein simply as “processors”), one or morecommunication interfaces, one or more display units, and one or moreuser input devices. The memory may include any computer-readable media,and may store computer instructions (also referred to herein as“processor-executable instructions”) for implementing the variousfunctionalities described herein. The processing unit(s) may be used toexecute the instructions. The communication interface(s) may be coupledto a wired or wireless network, bus, or other communication means andmay therefore allow the computer to transmit communications to and/orreceive communications from other devices. The display unit(s) may beprovided, for example, to allow a user to view various information inconnection with execution of the instructions. The user input device(s)may be provided, for example, to allow the user to make manualadjustments, make selections, enter data or various other information,and/or interact in any of a variety of manners with the processor duringexecution of the instructions.

The various methods or processes outlined herein may be coded assoftware that is executable on one or more processors that employ anyone of a variety of operating systems or platforms. Additionally, suchsoftware may be written using any of a number of suitable programminglanguages and/or programming or scripting tools, and also may becompiled as executable machine language code or intermediate code thatis executed on a framework or virtual machine.

In this respect, various inventive concepts may be embodied as acomputer readable storage medium (or multiple computer readable storagemedia) (e.g., a computer memory, one or more floppy discs, compactdiscs, optical discs, magnetic tapes, flash memories, circuitconfigurations in Field Programmable Gate Arrays or other semiconductordevices, or other non-transitory medium or tangible computer storagemedium) encoded with one or more programs that, when executed on one ormore computers or other processors, perform methods that implement thevarious embodiments of the invention discussed above. The computerreadable medium or media can be transportable, such that the program orprograms stored thereon can be loaded onto one or more differentcomputers or other processors to implement various aspects of thepresent invention as discussed above.

The terms “program” or “software” are used herein in a generic sense torefer to any type of computer code or set of computer-executableinstructions that can be employed to program a computer or otherprocessor to implement various aspects of embodiments as discussedabove. Additionally, it should be appreciated that according to oneaspect, one or more computer programs that when executed perform methodsof the present invention need not reside on a single computer orprocessor, but may be distributed in a modular fashion amongst a numberof different computers or processors to implement various aspects of thepresent invention.

Computer-executable instructions may be in many forms, such as programmodules, executed by one or more computers or other devices. Generally,program modules include routines, programs, objects, components, datastructures, etc. that perform particular tasks or implement particularabstract data types. Typically the functionality of the program modulesmay be combined or distributed as desired in various embodiments.

Also, data structures may be stored in computer-readable media in anysuitable form. For simplicity of illustration, data structures may beshown to have fields that are related through location in the datastructure. Such relationships may likewise be achieved by assigningstorage for the fields with locations in a computer-readable medium thatconvey relationship between the fields. However, any suitable mechanismmay be used to establish a relationship between information in fields ofa data structure, including through the use of pointers, tags or othermechanisms that establish relationship between data elements.

Also, various inventive concepts may be embodied as one or more methods,of which an example has been provided. The acts performed as part of themethod may be ordered in any suitable way. Accordingly, embodiments maybe constructed in which acts are performed in an order different thanillustrated, which may include performing some acts simultaneously, eventhough shown as sequential acts in illustrative embodiments.

As used herein, natural scene is to be understood to refer to an imageof a natural environment, e.g., as described in Geisler WS Visualperception and the statistical of properties of natural scenes. AnnuRev. Psychol. 59:167-92 (2008). In some embodiments, natural scenes maybe replaced with any suitable complex image, e.g., an imagecharacterized by a spatial and/or temporal frequency power spectrum thatgenerally conforms to a inverse frequency squared law. In someembodiments, e.g., where a short video clip is used, the spectrum of thecomplex image may deviate somewhat from the inverse square law. Forexample, in some embodiments, the complex image may have a spatial ortemporal a power spectrum of the form 1/f^x, where f is the frequencyand x is in the range of, e.g., 1-3, or any subrange thereof (e.g.1.5-2.5, 1.75-2.25, 1.9-2.1, etc.)

A white noise image refers to a noise image having a spatial frequencypower spectrum that is essentially flat.

As used herein the term “light” and related terms (e.g. “optical”,“visual”) are to be understood to include electromagnetic radiation bothwithin and outside of the visible spectrum, including, for example,ultraviolet and infrared radiation.

The indefinite articles “a” and “an,” as used herein in thespecification and in the claims, unless clearly indicated to thecontrary, should be understood to mean “at least one.”

The phrase “or,” as used herein in the specification and in the claims,should be understood to mean “either or both” of the elements soconjoined, i.e., elements that are conjunctively present in some casesand disjunctively present in other cases. Multiple elements listed with“or” should be construed in the same fashion, i.e., “one or more” of theelements so conjoined. Other elements may optionally be present otherthan the elements specifically identified by the “or” clause, whetherrelated or unrelated to those elements specifically identified. Thus, asa non-limiting example, a reference to “A or B”, when used inconjunction with open-ended language such as “including” can refer, inone embodiment, to A only (optionally including elements other than B);in another embodiment, to B only (optionally including elements otherthan A); in yet another embodiment, to both A and B (optionallyincluding other elements); etc.

As used herein in the specification and in the claims, “or” should beunderstood to have the same meaning as “or” as defined above. Forexample, when separating items in a list, “or” or “or” shall beinterpreted as being inclusive, i.e., the inclusion of at least one, butalso including more than one, of a number or list of elements, and,optionally, additional unlisted items. Only terms clearly indicated tothe contrary, such as “only one of” or “exactly one of,” or, when usedin the claims, “consisting of,” will refer to the inclusion of exactlyone element of a number or list of elements. In general, the term “or”as used herein shall only be interpreted as indicating exclusivealternatives (i.e. “one or the other but not both”) when preceded byterms of exclusivity, such as “either,” “one of,” “only one of,” or“exactly one of” “Consisting essentially of,” when used in the claims,shall have its ordinary meaning as used in the field of patent law.

In the claims, as well as in the specification above, all transitionalphrases such as “including,” “including,” “carrying,” “having,”“containing,” “involving,” “holding,” “composed of,” and the like are tobe understood to be open-ended, i.e., to mean including but not limitedto. Only the transitional phrases “consisting of” and “consistingessentially of” shall be closed or semi-closed transitional phrases,respectively, as set forth in the United States Patent Office Manual ofPatent Examining Procedures, Section 2111.03.

All definitions, as defined and used herein, should be understood tocontrol over dictionary definitions, definitions in documentsincorporated by reference, and/or ordinary meanings of the definedterms.

Variations, modifications and other implementations of what is describedherein will occur to those of ordinary skill in the art withoutdeparting from the spirit and scope of the invention. While certainembodiments of the present invention have been shown and described, itwill be obvious to those skilled in the art that changes andmodifications may be made without departing from the spirit and scope ofthe invention. The matter set forth in the foregoing description andaccompanying drawings is offered by way of illustration only and not asa limitation.

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What is claimed is:
 1. A method comprising: receiving, by a processingdevice, raw image data corresponding to a series of raw images; andprocessing the raw image data with an encoder of the processing deviceto generate encoded data, wherein the encoder is characterized by aninput/output transformation that substantially mimics the input/outputtransformation of at least one retinal cell a vertebrate retina; whereinthe processing the raw image data comprises applying a spatiotemporaltransformation to a set of images to generate a set of retinal responsevalues, and wherein the applying the spatiotemporal transformationfurther comprises: applying a spatiotemporal kernel to the set of imagesto generate spatially-temporally transformed images; and applying anonlinear function to the spatially-temporally transformed images togenerate the set of retinal response values; generating the encoded databased on the set of retinal response values; and activating a highresolution signaling device according to the encoded data.
 2. The methodof claim 1, wherein processing the raw image data with an encoder togenerate encoded data comprises: processing the raw image data togenerate a plurality of values, X, transforming the plurality of Xvalues into a plurality of response values, λ_(m), indicative of acorresponding response of a retinal cell in the retina, m, andgenerating the encoded data based on the response values.
 3. The methodof claim 2, wherein the response values correspond to retinal cellfiring rates.
 4. The method of claim 3, wherein the response valuescorrespond to a function of the retinal cell firing rates.
 5. The methodof claim 3, wherein the response values correspond to retinal celloutput pulses.
 6. The method of claim 3, wherein the response valuescorrespond to retinal cell generator potential.
 7. The method of claim1, wherein processing the raw image data with an encoder to generateencoded data comprises: receiving images from the raw image data and,for each image, rescaling the luminance or contrast to generate arescaled image stream; receiving a set of N rescaled images from therescaled image stream and applying the spatiotemporal transformation tothe set of N images to generate the set of retinal response values, eachvalue in the set corresponding to a respective one of the retinal cells.8. The method of claim 7, wherein the response values comprise retinacell firing rates.
 9. The method of claim 7 wherein N is at least
 5. 10.The method of claim 7 wherein N is at least
 20. 11. The method of claim7, wherein applying the spatiotemporal kernel comprises: convolving ofthe N rescaled images with the spatiotemporal kernel to generate Nspatially-temporally transformed images.
 12. The method of claim 11,wherein applying the spatiotemporal kernel comprises: convolving the Nrescaled images with a spatial kernel to generate N spatiallytransformed images; convolving the N spatially transformed images with atemporal kernel to generate a temporal transformation output; andapplying a nonlinear function to the temporal transformation output togenerate the set of retinal response values.
 13. The method of claim 1,wherein the encoder is characterized by a set of parameters, and whereinthe values of the parameters are determined using response data obtainedexperimentally from a mammalian retina while said retina is exposed towhite noise and natural scene stimuli.
 14. The method of claim 13,wherein the encoder is configured such that the Pearson's correlationcoefficient between a test input stimulus and a corresponding stimulusreconstructed from the encoded data that would be generated by theencoder in response to the test input stimulus is at least about 0.35.15. The method of claim 13, wherein the encoder is configured such thatthe Pearson's correlation coefficient between a test input stimulus anda corresponding stimulus reconstructed from the encoded data that wouldbe generated by the encoder in response to the test input stimulus is atleast about 0.65.
 16. The method of claim 13, wherein the encoder isconfigured such that the Pearson's correlation coefficient between atest input stimulus and a corresponding stimulus reconstructed from theencoded data that would be generated by the encoder in response to thetest input stimulus is at least about 0.95.
 17. The method of claim 13,wherein the test input stimulus comprises a series of natural scenes.